HCF and LCM PYQs
Overview
This page provides comprehensive Class 10 Maths HCF and LCM PYQs | Real Numbers. HCF and LCM previous year questions for Class 10 Maths Real Numbers. Practice CBSE board PYQs with step-by-step solutions on SJMaths.
Practice Previous Year Questions Topic-wise
Q10
2022
00:00
How many decimal places will the expansion of $\frac{23}{2^2 \times 5}$ have?
The denominator is $2^2 \times 5^1$.
The maximum power of 2 or 5 in the denominator is 2 (from $2^2$).
Therefore, the decimal expansion will terminate after 2 decimal places.
Calculation: $\frac{23}{2^2 \times 5} = \frac{23 \times 5}{2^2 \times 5^2} = \frac{115}{100} = 1.15$
Final Answer: 2 decimal places
Q12
2020
00:00
The decimal expansion of $\frac{17}{8}$ will terminate after how many decimal places?
Denominator $8 = 2^3$.
The maximum power is 3.
So it will terminate after 3 decimal places.
Calculation: $\frac{17}{8} = \frac{17 \times 5^3}{2^3 \times 5^3} = \frac{17 \times 125}{1000} = \frac{2125}{1000} = 2.125$
Final Answer: 3 decimal places
Q16
2017
00:00
Does $\frac{2\sqrt{45} + 3\sqrt{20}}{2\sqrt{5}}$ simplify to a rational or irrational number?
Simplify the numerators:
$\sqrt{45} = \sqrt{9 \times 5} = 3\sqrt{5}$
$\sqrt{20} = \sqrt{4 \times 5} = 2\sqrt{5}$
Numerator $= 2(3\sqrt{5}) + 3(2\sqrt{5}) = 6\sqrt{5} + 6\sqrt{5} = 12\sqrt{5}$
Expression $= \frac{12\sqrt{5}}{2\sqrt{5}} = \frac{12}{2} = 6$
6 is a rational number.
Final Answer: Rational number
Q25
2017
00:00
Without long division, state whether $\frac{17}{3125}$ is terminating or non-terminating repeating. Give reasons.
Factorize the denominator: $3125 = 5^5$.
The denominator is of the form $2^n \times 5^m$ (where $n=0, m=5$).
Since it has no prime factors other than 2 or 5, the decimal expansion is terminating.
Final Answer: Terminating
Q32
2023
00:00
(a) Three alarm clocks ring at intervals of 4, 12 and 20 minutes. If they ring together at 12:00 noon, at what time will they next ring together? 3 Marks
(b) Find the HCF of 612 and 1314 using the prime factorisation method. 2 Marks
(0) [object Object]
(1) [object Object]
(b) Find the HCF of 612 and 1314 using the prime factorisation method. 2 Marks
(0) [object Object]
(1) [object Object]
Q33
2022
00:00
(a) Find the largest number that divides 125, 162 and 259 leaving remainders 5, 6 and 7 respectively.
(b) An army contingent of 678 soldiers marches behind a band of 36 members. Both groups march in the same number of columns. Find the maximum number of columns.
(0) [object Object]
(1) [object Object]
(b) An army contingent of 678 soldiers marches behind a band of 36 members. Both groups march in the same number of columns. Find the maximum number of columns.
(0) [object Object]
(1) [object Object]
Q34
2021
00:00
(a) On a morning walk, three persons step off together. Their steps measure 40 cm, 42 cm and 45 cm. What is the minimum distance each should walk so that each can cover the distance in complete steps?
(b) There are 576 boys and 448 girls in a school to be divided into equal sections of either boys or girls only. Find the total number of sections formed.
(0) [object Object]
(1) [object Object]
(b) There are 576 boys and 448 girls in a school to be divided into equal sections of either boys or girls only. Find the total number of sections formed.
(0) [object Object]
(1) [object Object]
Q35
2024
00:00
CASE STUDY: A mathematics teacher asked students to collect different coloured buttons. Meera collected 72 red, 48 blue and 108 green buttons. She wants to pack them into packets such that each packet has the same number of buttons of the same colour.
(i) Find the HCF of 72, 48 and 108.
(ii) Find the LCM of 72, 48 and 108.
(iii) What is the maximum number of buttons in each packet? Also find the total number of packets formed.
(0) [object Object]
(1) [object Object]
(2) [object Object]
(i) Find the HCF of 72, 48 and 108.
(ii) Find the LCM of 72, 48 and 108.
(iii) What is the maximum number of buttons in each packet? Also find the total number of packets formed.
(0) [object Object]
(1) [object Object]
(2) [object Object]
Q36
2023
00:00
CASE STUDY: A school is organizing a Sports Day event. Students of Class 6, 7 and 8 are to march in rows. The number of students in Class 6, 7 and 8 are 96, 240 and 336 respectively. The principal wants the maximum number of students in each row with each row consisting of students of the same class only.
(i) Find the HCF of 96 and 240.
(ii) Find the HCF of 96, 240 and 336.
(iii) Find the maximum number of rows formed in the march.
(0) [object Object]
(1) [object Object]
(2) [object Object]
(i) Find the HCF of 96 and 240.
(ii) Find the HCF of 96, 240 and 336.
(iii) Find the maximum number of rows formed in the march.
(0) [object Object]
(1) [object Object]
(2) [object Object]
Q37
2022
00:00
CASE STUDY: A morning walk is considered good for health. Three friends Anjali, Babita and Chandni step off together and their steps measure 80 cm, 85 cm and 90 cm respectively. They walk on a straight path.
(i) Find the HCF of step lengths 80 cm and 85 cm.
(ii) What is the minimum distance Anjali should walk so that she completes her steps exactly?
(iii) What is the minimum distance all three should walk so that each completes their steps exactly?
(0) [object Object]
(1) [object Object]
(2) [object Object]
(i) Find the HCF of step lengths 80 cm and 85 cm.
(ii) What is the minimum distance Anjali should walk so that she completes her steps exactly?
(iii) What is the minimum distance all three should walk so that each completes their steps exactly?
(0) [object Object]
(1) [object Object]
(2) [object Object]
Q38
2021
00:00
CASE STUDY: A librarian has 204 English books, 306 Hindi books and 136 Sanskrit books. She wants to arrange the books in shelves such that each shelf contains the same number of books and all books on a shelf are of the same language.
(i) Find the prime factorisation of 204.
(ii) Find the HCF of 204, 306 and 136.
(iii) What is the maximum number of books on each shelf? Find also the minimum number of shelves required.
(0) [object Object]
(1) [object Object]
(2) [object Object]
(i) Find the prime factorisation of 204.
(ii) Find the HCF of 204, 306 and 136.
(iii) What is the maximum number of books on each shelf? Find also the minimum number of shelves required.
(0) [object Object]
(1) [object Object]
(2) [object Object]
How many decimal places will the expansion of $\frac{23}{2^2 \times 5}$ have?
The denominator is $2^2 \times 5^1$.
The maximum power of 2 or 5 in the denominator is 2 (from $2^2$).
Therefore, the decimal expansion will terminate after 2 decimal places.
Calculation: $\frac{23}{2^2 \times 5} = \frac{23 \times 5}{2^2 \times 5^2} = \frac{115}{100} = 1.15$
Final Answer: 2 decimal places
Q12
2020
00:00
The decimal expansion of $\frac{17}{8}$ will terminate after how many decimal places?
Denominator $8 = 2^3$.
The maximum power is 3.
So it will terminate after 3 decimal places.
Calculation: $\frac{17}{8} = \frac{17 \times 5^3}{2^3 \times 5^3} = \frac{17 \times 125}{1000} = \frac{2125}{1000} = 2.125$
Final Answer: 3 decimal places
Q16
2017
00:00
Does $\frac{2\sqrt{45} + 3\sqrt{20}}{2\sqrt{5}}$ simplify to a rational or irrational number?
Simplify the numerators:
$\sqrt{45} = \sqrt{9 \times 5} = 3\sqrt{5}$
$\sqrt{20} = \sqrt{4 \times 5} = 2\sqrt{5}$
Numerator $= 2(3\sqrt{5}) + 3(2\sqrt{5}) = 6\sqrt{5} + 6\sqrt{5} = 12\sqrt{5}$
Expression $= \frac{12\sqrt{5}}{2\sqrt{5}} = \frac{12}{2} = 6$
6 is a rational number.
Final Answer: Rational number
Q25
2017
00:00
Without long division, state whether $\frac{17}{3125}$ is terminating or non-terminating repeating. Give reasons.
Factorize the denominator: $3125 = 5^5$.
The denominator is of the form $2^n \times 5^m$ (where $n=0, m=5$).
Since it has no prime factors other than 2 or 5, the decimal expansion is terminating.
Final Answer: Terminating
Q32
2023
00:00
(a) Three alarm clocks ring at intervals of 4, 12 and 20 minutes. If they ring together at 12:00 noon, at what time will they next ring together? 3 Marks
(b) Find the HCF of 612 and 1314 using the prime factorisation method. 2 Marks
(0) [object Object]
(1) [object Object]
(b) Find the HCF of 612 and 1314 using the prime factorisation method. 2 Marks
(0) [object Object]
(1) [object Object]
Q33
2022
00:00
(a) Find the largest number that divides 125, 162 and 259 leaving remainders 5, 6 and 7 respectively.
(b) An army contingent of 678 soldiers marches behind a band of 36 members. Both groups march in the same number of columns. Find the maximum number of columns.
(0) [object Object]
(1) [object Object]
(b) An army contingent of 678 soldiers marches behind a band of 36 members. Both groups march in the same number of columns. Find the maximum number of columns.
(0) [object Object]
(1) [object Object]
Q34
2021
00:00
(a) On a morning walk, three persons step off together. Their steps measure 40 cm, 42 cm and 45 cm. What is the minimum distance each should walk so that each can cover the distance in complete steps?
(b) There are 576 boys and 448 girls in a school to be divided into equal sections of either boys or girls only. Find the total number of sections formed.
(0) [object Object]
(1) [object Object]
(b) There are 576 boys and 448 girls in a school to be divided into equal sections of either boys or girls only. Find the total number of sections formed.
(0) [object Object]
(1) [object Object]
Q35
2024
00:00
CASE STUDY: A mathematics teacher asked students to collect different coloured buttons. Meera collected 72 red, 48 blue and 108 green buttons. She wants to pack them into packets such that each packet has the same number of buttons of the same colour.
(i) Find the HCF of 72, 48 and 108.
(ii) Find the LCM of 72, 48 and 108.
(iii) What is the maximum number of buttons in each packet? Also find the total number of packets formed.
(0) [object Object]
(1) [object Object]
(2) [object Object]
(i) Find the HCF of 72, 48 and 108.
(ii) Find the LCM of 72, 48 and 108.
(iii) What is the maximum number of buttons in each packet? Also find the total number of packets formed.
(0) [object Object]
(1) [object Object]
(2) [object Object]
Q36
2023
00:00
CASE STUDY: A school is organizing a Sports Day event. Students of Class 6, 7 and 8 are to march in rows. The number of students in Class 6, 7 and 8 are 96, 240 and 336 respectively. The principal wants the maximum number of students in each row with each row consisting of students of the same class only.
(i) Find the HCF of 96 and 240.
(ii) Find the HCF of 96, 240 and 336.
(iii) Find the maximum number of rows formed in the march.
(0) [object Object]
(1) [object Object]
(2) [object Object]
(i) Find the HCF of 96 and 240.
(ii) Find the HCF of 96, 240 and 336.
(iii) Find the maximum number of rows formed in the march.
(0) [object Object]
(1) [object Object]
(2) [object Object]
Q37
2022
00:00
CASE STUDY: A morning walk is considered good for health. Three friends Anjali, Babita and Chandni step off together and their steps measure 80 cm, 85 cm and 90 cm respectively. They walk on a straight path.
(i) Find the HCF of step lengths 80 cm and 85 cm.
(ii) What is the minimum distance Anjali should walk so that she completes her steps exactly?
(iii) What is the minimum distance all three should walk so that each completes their steps exactly?
(0) [object Object]
(1) [object Object]
(2) [object Object]
(i) Find the HCF of step lengths 80 cm and 85 cm.
(ii) What is the minimum distance Anjali should walk so that she completes her steps exactly?
(iii) What is the minimum distance all three should walk so that each completes their steps exactly?
(0) [object Object]
(1) [object Object]
(2) [object Object]
Q38
2021
00:00
CASE STUDY: A librarian has 204 English books, 306 Hindi books and 136 Sanskrit books. She wants to arrange the books in shelves such that each shelf contains the same number of books and all books on a shelf are of the same language.
(i) Find the prime factorisation of 204.
(ii) Find the HCF of 204, 306 and 136.
(iii) What is the maximum number of books on each shelf? Find also the minimum number of shelves required.
(0) [object Object]
(1) [object Object]
(2) [object Object]
(i) Find the prime factorisation of 204.
(ii) Find the HCF of 204, 306 and 136.
(iii) What is the maximum number of books on each shelf? Find also the minimum number of shelves required.
(0) [object Object]
(1) [object Object]
(2) [object Object]