HCF AND LCM WORKSHEETS 1

About HCF and LCM worksheets 1

In this HCF and LCM worksheets 1,we give the questions on HCF and LCM whose qualities  are in high standard and practicing these questions will definitely make the students to score marks in HCF and LCM. 

Example Quiz 1


1. Find the HCF of 23x32x5x74, 22x35x52x76, 23x53x72

(A) 979

(B) 980

(C) 981

(D) 982


2. Find the LCM of 22x33x5 , 23x32x52, 2x3x52

(A) 5400

(B) 5410

(C) 5420

(D) 5430


3. Find the H.C.F of 0.63, 1.05, and 2.1

(A) 0.21

(B) 0.22

(C) 0.23

(D) 0.24


4. Two numbers are in the ratio of 15:11. If their HCF is 13, find the numbers.

(A) 196 and 144

(B) 196 and 143

(C) 195 and 144

(D) 195 and 143


5. The HCF of two numbers is 11 and their LCM is 693. If one of the numbers is 77, find the other.

(A) 99

(B) 88

(C) 77

(D) 66


6. Find the L.C.M of 16, 24, 36 and 54.

(A) 430

(B) 431

(C) 432

(D) 433


7. Find the H.C.F of 513, 1134, and 1215.

(A) 27

(B) 28

(C) 29

(D) 30


8. Find the greatest possible length which can be used to measure exactly the lengths 4 m 95 cm, 9 m and 16 m 65 cm.

(A) 45 cm

(B) 44 cm

(C) 43 cm

(D) 42 cm


9. Find the greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively.

(A) 126

(B) 127

(C) 128

(D) 129


10. Find the largest number which divides 62, 132 and 237 leaves the same remainder in each case.

(A) 32

(B) 33

(C) 34

(D) 35




Question No.1

Question No.2

Question No.3

Question No.4

Question No.5

Question No.6

Question No.7

Question No.8

Question No.9

Question No.10


jQuery UI Accordion - Default functionality
23x32x5x74, 22x35x52x76, 23x53x72

In the above given numbers, we find 2, 5 and 7 in common.
Take 2, 5 and 7 with minimum power. That is 22, 5, 72

Now, H.C.F = 22x5x72 = 980


jQuery UI Accordion - Default functionality
22x33x5 , 23x32x52, 2x3x52

In the above given numbers, take all prime factors with maximum power.

They are, 23, 33, 52

Now, L.C.M = 23x33x52 = 5400


jQuery UI Accordion - Default functionality
We we look in to the given numbers 0.63, 1.05, and 2.1, maximum number of digits after the decimal is 2.

So, let us multiply each number by 100 to avoid decimal.

When the given numbers are multiplied by100, we get 63, 105, 210

63 = 32x7
105 = 5x3x7
210 = 2x5x3x7

In the prime factors (63, 105, 210), we find 3 and 7 in common
Take 3 and 7 with minimum power. They are 31 and 71

Now, H.C.F of (63, 105, 210) = 31x71 = 21

To get H.C.F of (0.63, 1.05, 2.1), divide 21 by 100. 21/100 = 0.21

Therefore, H.C.F of (0.63, 1.05, 2.1) = 0.21


jQuery UI Accordion - Default functionality
From the given ratio, two numbers are 15x and 11x.

H.C.F of 15x and 11x = x ---(1)

Given : H.C.F of two numbers = 13 ---(2)

From(1)& (2), we get x = 13

15x = 15(13) = 195
11x = 11(13) = 143

Hence, the two numbers are 195 and 143


jQuery UI Accordion - Default functionality
Given: One of the numbers = 77, H.C.F = 11 and L.C.M = 693

Let "x" be the other number.

Product of two numbers = Product of their H.C.F and L.C.M
77x = 11X693

x = 99

Hence, the other number is 99


jQuery UI Accordion - Default functionality
Given numbers are 16, 24, 36, 54

16 = 24
24 = 23x3
36 = 22x32
54 = 2x33

In the above prime factors of (16, 24, 36, 54), take all prime factors with maximum power. They are 24 and 33

Now, L.C.M = 24x33 = 432


jQuery UI Accordion - Default functionality
Given numbers are 513, 1134, 1215

513 = 33x19
1134 = 2x34x7
1215 = 35x5

In the above prime factors of (513, 1134, 1215), we find 3 in common.So, take 3 with minimum power. That is 33

Now, H.C.F = 33 = 27


jQuery UI Accordion - Default functionality
Required greatest possible length = H.C.F of (495, 900, 1665)

495 = 32x5x11
900 = 22x32x52
1665 = 32x5x37

In the prime factors of (495, 900, 1665), we find 3 and 5 in common. Take 3 and 5 with minimum power.
They are 32 and 5

Now, H.C.F = 32x5 = 45

Hence, the required greatest possible length is 45 cm


jQuery UI Accordion - Default functionality
Required greatest number = H.C.F. of (1657 - 6) and (2037 - 5)

= H.C.F. of (1651, 2032) = 127.


jQuery UI Accordion - Default functionality
Required Number = H.C.F of [(132-62), (237-132), and (237-62)]

= H.C.F of [70, 105, 175] = 35

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jQuery UI Accordion - Default functionality
For each divisor and corresponding remainder, we have to find the difference.

35-25=10
45-35=10
55-45=10

we get the difference 10 (for all divisors and corresponding remainders)

Now we have to find the L.C.M of (35,45,55) and subtract the difference from the L.C.M.

L.C.M of (35,45,55) = 3465

Hence the required least number = 3465-10 = 3455