Question

2. Find the LCM of the followingnumbers by the prime factorisation method . 60, 28, 36, 45 viii. 112, 168, 266​

Answer 1

Answer:

Hey There!

LCM of 60, 28, 36 and 45-

List all prime factors for each number.

Prime Factorization of 28 is:

2 x 2 x 7  =>  22 x 71

Prime Factorization of 36 is:

2 x 2 x 3 x 3  =>  22 x 32

Prime Factorization of 45 is:

3 x 3 x 5  =>  32 x 51

Prime Factorization of 60 is:

2 x 2 x 3 x 5  =>  22 x 31 x 51

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

The new superset list is

2, 2, 3, 3, 5, 7

Multiply these factors together to find the LCM.

LCM = 2 x 2 x 3 x 3 x 5 x 7 = 1260

In exponential form:  LCM = 22 x 32 x 51 x 71 = 1260

LCM = 1260

Therefore,  LCM(28, 36, 45, 60) = 1260

LCM of 112, 168, and 266-

List all prime factors for each number.

Prime Factorization of 112 is:

2 x 2 x 2 x 2 x 7  =>  24 x 71

Prime Factorization of 168 is:

2 x 2 x 2 x 3 x 7  =>  23 x 31 x 71

Prime Factorization of 266 is:

2 x 7 x 19  =>  21 x 71 x 191

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

The new superset list is

2, 2, 2, 2, 3, 7, 19

Multiply these factors together to find the LCM.

LCM = 2 x 2 x 2 x 2 x 3 x 7 x 19 = 6384

In exponential form:  LCM = 24 x 31 x 71 x 191 = 6384

LCM = 6384

Therefore,   LCM (112, 168, 266) = 6384

Hey Mate, Hope This Helps You!

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