The L.C.M. of $(5^{3} - 3^{3})$ and $(4^{3} - 2^{3})$ is:

475

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392

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210

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1176

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Solution

The correct option is B $392$
Let us first solve the given subtractions as follows:

$5^{3} - 3^{3} = 125 - 27 = 98$

$4^{3} - 2^{3} = 64 - 8 = 56$

Now, factorize $98$ and $56$ as shown below:

$98 = 2 \times 7 \times 7 56 = 2 \times 2 \times 2 \times 7$

We know that the least common multiple (LCM) of two numbers is the smallest number that they both divide evenly into.

Therefore, the LCM of $98$ and $56$ is:

LCM $= 2 \times 2 \times 2 \times 7 \times 7 = 392$

Hence, the LCM of $(5^{3} - 3^{3})$ and $(4^{3} - 2^{3})$ is $392$

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