Question

which is the smallest number divisible by 18, 24 and 32.
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Answer 1

Answer:

the smallest no divisible by 18,24,32

= 1152

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Answer 2

PRIME FACTORIZATION

List all prime factors for each number.

Prime Factorization of 18 is:

2 x 3 x 3  =>  21 x 32

Prime Factorization of 24 is:

2 x 2 x 2 x 3  =>  23 x 31

Prime Factorization of 32 is:

2 x 2 x 2 x 2 x 2  =>  25

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, 2, 3, 3

Multiply these factors together to find the LCM.

LCM = 2 x 2 x 2 x 2 x 2 x 3 x 3 = 288

In exponential form:

LCM = 25 x 32 = 288

LCM = 288

Therefore,

LCM(18, 24, 32) = 288