Practice the questions given in the worksheet on methods of hcf and lcm. We know full form of hcf is known as highest common factor and lcm is known as least common multiple.

**I.** Fill in the blanks:

(i) Even numbers are the multiples of ________.

(ii) 24 is an even number but 29 is an ________ number.

(iii) ________ is neither prime nor composite number.

(iv) ________ is the only even prime number.

(v) The smallest prime number is ________.

(vi) The smallest odd composite number is ________.

(vii) There are ________ prime numbers between 1 and 15.

**II.** Write the first four multiples of the following:

(i) 6

(ii) 8

(iii) 9

(iv) 12

(v) 15

**III.** Write the prime factors of the following:

(i) 50

(ii) 49

(iii) 70

(iv) 90

(v) 96

**IV.** Test whether the numbers in red color are the multiples
of the numbers in blue color. Put (√) if yes, and (X) if no in the blank space.

(i) 40 3 ____

(ii) 75 5 ____

(iii) 49 6 ____

(iv) 99 9 ____

(v) 48 7 ____

(vi) 50 2 ____

**V.** Encircle the common multiples for each set of the
numbers.

(i) 3, 6, 9, 12, 15, 21, 27, 36, 48, 45

6, 18, 24, 30, 36, 48, 54, 60

(ii) 2, 6, 8, 10, 14, 18, 20, 24, 30

5, 10, 15, 20, 30, 35, 55, 60, 75

**VI.** Find the number which is 2 more than the L.C.M. of each
of the following.

(i) 4, 8, 14

(ii) 5, 7, 15

(iii) 25, 45, 15

(iv) 42, 48, 54

**VII.** Find the number which is 2 less than the H.C.F. of each
of the following.

(i) 25, 45, 60

(ii) 70, 85, 45

(iii) 40, 120, 150

(iv) 15, 30, 45

**VIII.** Mike multiplied two numbers and got 64 as their products. If the L.C.M. of these two numbers are 32, find the H.C.F. of the numbers.

Answers for the worksheet on methods of hcf and lcm are given below.

**Answers:**

**I.** (i) 2

(ii) odd

(iii) 1

(iv) 2

(v) 2

(vi) 9

(vii) 6

**II.** (i) 6, 12, 18, 24

(ii) 8, 16, 24, 32

(iii) 9, 18, 27, 36

(iv) 12, 24, 36, 48

(v) 15, 30, 45, 60

**III.** (i) 2 × 5 × 5

(ii) 7 × 7

(iii) 2 × 5 × 7

(iv) 2 × 5 × 9

(v) 2 × 2 × 2 × 2 × 2 × 3

**IV.** (i) X

(ii) √

(iii) X

(iv) √

(v) X

(vi) √

**V.** (i) 6, 36, 48, 6, 36, 48

(ii) 10, 20, 30, 10, 20, 30

VI. (i) 58

(ii) 107

(iii) 227

(iv) 3026

**VII.** (i) 3

(ii) 3

(iii) 8

(iv) 13

**VIII.** 2

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