Question

Find the L.C.M of 144, 180 and 192 by prime factorisation method.​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

List all prime factors for each number.

Prime Factorization of 144 is:

2 x 2 x 2 x 2 x 3 x 3  =>  2^4 x 3^2

Prime Factorization of 180 is:

2 x 2 x 3 x 3 x 5  =>  2^2 x 3^2 x 5^1

Prime Factorization of 192 is:

2 x 2 x 2 x 2 x 2 x 2 x 3  =>  2^6 x 3^1

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 list is

2, 2, 2, 2, 2, 2, 3, 3, 5

Multiply these factors together to find the LCM.

LCM = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 = 2880

In exponential form:

LCM = 2^6 x 3^2 x 5^1 = 2880

LCM = 2880

Therefore,

LCM(144, 180, 192) = 2880

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