Question

# $18$ is divisible by both $2$ and $3.$. It is also divisible by $2x3=6.$ Similarly, a number is divisble by $4$ and $6$. Can we say that the number must be divisible by $4x6=24?$ If not, give an example to justify your answer.

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Solution

## Let us consider the numbers which are divisible by $4$$4,8,12,16,20,24,28,32,36,40\dots .$Now let us consider the numbers which are divisible by $6$$6,12,18,24,30,36,42,48,54,60,\dots \dots .$So the number divisible by both $4$ and $6$ are$12,24,\dots \dots .$But we can observe that number $12,36,\dots$are divisible by both $4$ and $6$ but not divisible by $24.$Hence$,$ it is concluded that a number divisible by $4$ and $6$ is not divisible by $24.$

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