Question

Find the largest number that always divides the product of 3 consecutive multiples of 4?​

Answer 1

Answer:

This question can be solved rather easily by TESTing VALUES. IF... the three consecutive multiples of 4 are 4, 8 and 12, then the PRODUCT of those 3 numbers is (4)(8)(12) = 384

Step-by-step explanation:

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Answer 2

The three consecutive multiples of 4 are

$4m,4(m+1),4(m+2)$

Their product will be:

$& =4m\times 4(m+1)\times 4(m+2) \\ & =64m\times (m+1)\times (m+2)$

By putting $m=1$, we will get the largest number that will always divide the product of 3 consecutive multiples of 4

Therefore,

$& =64\times (1+1)\times (1+2) \\ & =64\times 2\times 3 \\ & =384$

Hence, the largest number that always divides the product of 3 consecutive multiples $4$ is $384$.