# LCM and HCF Questions

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LCM of:

Here are some samples of LCM of Numbers calculations.

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HCF of:

Here are some samples of HCF of Numbers calculations.

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Practice the HCF and LCM Related Questions in advance so that you can attempt them with confidence in your tests. Acquire essential ideas to solve the difficult questions on LCM and HCF too easily within a split second.

## List of LCM and HCF Questions with Answers

1. What is the H.C.F. of 513, 1134 and 1215 _____________

a. 18

b. 27

c. 33

d. 36

Answer

Answer: (b)

Explanation:

HCF of 513, 1134, 1215 is obtained by Factorization as such

The factors of 513 are 1, 3, 9, 19, 27, 57, 171, 513

The factors of 1134 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 81, 126, 162, 189, 378, 567, 1134

The factors of 1215 are 1, 3, 5, 9, 15, 27, 45, 81, 135, 243, 405, 1215

Then the Highest Common Factor or Greatest Common Factor is 27

2. Find the LCM of 1.05 and 2.1

a. 1.3

b. 1.25

c. 2.1

d. 4.30

Answer

Answer: (c)

Explanation:

If the Numbers are in Decimal Format change them to non-decimal format and the numbers become 105 and 210.

Now take the LCM(105, 210)

LCM(105, 210) = 210 the smallest number that divides both of them.

Now change the result obtained back to decimal format i.e. 2.1

3. Find LCM of three fractions 36/225, 48/150, 72/65?

a. 72/225

b. 36/65

c. 144/5

d. 288/5

Answer

Answer: (c)

Explanation:

LCM of Fractions = LCM of Numerators/HCF of Denominators

LCM of Numerators means LCM(36, 48, 72) i.e. 144

HCF of Denominators means HCF(225, 150, 65) i.e. 5

LCM of Fractions = 144/5

4. What is the LCM of 25, 30, 35, and 40?

a. 3800

b. 4200

c. 4400

d. 3200

Answer

Answer: (b)

Explanation:

LCM of 25, 30, 35, and 40 using Prime Factorization Method

Prime Factorization of 25 is 5 x 5

Prime Factorization of 30 is 2 x 3 x 5

Prime Factorization of 35 is 5 x 7

Prime Factorization of 40 is 2 x 2 x 2 x 5

For each prime factor check for how many times the most often a factor occurs.

Multiply the factors to get the LCM

LCM = 2 x 2 x 2 x 3 x 5 x 5 x 7

= 4200

5. What is the greatest number that divides 639, 1065, and 1491 exactly?

a. 193

b. 183

c. 223

d. 213

Answer

Answer: (d)

Explanation:

HCF of 639, 1065, and 1491 is 213 the number that divides exactly all the three numbers exactly and leaves a remainder zero.

The two numbers A and B are in the ratio 5:6 such that their LCM is 480. Find their HCF?

a. 12

b. 16

c. 96

d. 240

Answer

Answer: (b)

Explanation:

If A, B are two numbers

A x B = HCF of A and B x LCM of A and B

Let us assume the common factor to be K so the 2 numbers become 5K and 6K

K is the HCF as 5, 6 don't have any common factors

5K*6K =480*K

Solving we get the value of K as 16 i.e. nothing but HCF or GCF.

7. Find the largest number that when divides 47, 35 and 27 leaves the same remainder. Also, find the value of the remainder?

a. 3, 4

b. 4, 3

c. 1, 9

d. 9, 1

Answer

Answer: ( b)

Among all the options available 4 is the number which when divides 47, 35, 27 the same remainder 1. The rest all leave different remainders.