Question

7. Find the LCM of the following by prime factorization method.
(a) 24 and 32
(b) 56 and 32
(c) 25 and 40​

Answer 1

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7a.) Answer:- 96

Explanation:-

LCM of 24 and 32 by Prime Factorization

Prime factorization of 24 and 32 is

(2 × 2 × 2 × 3) = 23 × 31 and (2 × 2 × 2 × 2 × 2) = 25 respectively.

Hence, the LCM of 24 and 32 by prime factorization is 96.

7b.)   Answer:- 224

Explanation:-   Prime factorization of 32 and 56 is

(2 × 2 × 2 × 2 × 2) = 25 and (2 × 2 × 2 × 7) = 23 × 71       respectively.

Hence, the LCM of 32 and 56 by prime factorization is 224

7c.)LCM of 25 and 40 by Prime Factorization

Prime factorization of 25 and 40 is

(5 × 5) = 52 and (2 × 2 × 2 × 5) = 23 × 51 respectively.

LCM of 25 and 40 can be obtained by multiplying prime factors raised to their respective highest power, i.e.

23 × 52 = 200.

Hence, the LCM of 25 and 40 by prime factorization is 200.

Answer 2

Answer:

a)24 and 32

LCM=2⁵×3=96

b)56 and 32

LCM=2⁵×7=448

c)25 and 40

LCM=2³×5²=200

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