Question

Suppose LCM(a,b)=7200. 15. Find the smallest possible value of b.

Answer 1

The smallest possible value of $b$ for a least common multiple of 7200 is 2.

Procedure - Least common multiple

Factor decomposition

The least common multiple is a whole number that is the least multiple of at least two whole numbers, to determine the smallest possible value of $b$ we need to make a factor decomposition, which is shown below:

$7200 = 2^{5}\times 3^2\times 5^2$

Final analysis - Smallest possible value

The smallest possible value of $b$ shall be the smallest possible prime numbers contained in the product. Thus, we conclude that the smallest possible value of $b$ is 2.

Result

The smallest possible value of $b$ for a least common multiple of 7200 is 2.

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