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Find the smallest length of a scale that can be divided into equal pieces of length 5m, 8m and 12m?

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120 m

100 m

115 m

150 m

answer is B.

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Detailed Solution

Here, we need to find the smallest length of the scale, such that it can be divided into equal pieces of length 5m, 8m, and 12m. That means the length of the scale must be the smallest common multiple of all three numbers.

That means, we need to find the Lowest Common Multiple (LCM) of all three numbers.

LCM of 5, 8, and 12:

First, reduce 5, 8, and 12 to their prime Factors:

5 = 5 x 1

8 = 2 x 2 x 2 = 2³

12 = 2 x 2 x 3 = 2² x 3

Considering the highest power of all factors we get,

LCM (5, 8, 12) = 5 x 2³ x 3 = 120

$∴$ The smallest length of a scale is 120 m that can be divided into equal pieces of length 5m, 8m and 12m.

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