For what value of M,is 34M divisible by 12? | vedclass

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(C) number is divisible by $12$ if it is divisible by both $3$ and $4$,since $12 = 3 	imes 4$.$(i)$ For divisibility by $3$,the sum of the digits mus

Vedclass · Accepted Answer

$8$

Vedclass · Answer

(C) number is divisible by $12$ if it is divisible by both $3$ and $4$,since $12 = 3 	imes 4$.$(i)$ For divisibility by $3$,the sum of the digits must be divisible by $3$. The sum of the digits of $34M$ is $3 + 4 + M = 7 + M$.If $M = 2$,sum $= 9$ (divisible by $3$).If $M = 5$,sum $= 12$ (divisible by $3$).If $M = 8$,sum $= 15$ (divisible by $3$).$(ii)$ For divisibility by $4$,the last two digits of the number must be divisible by $4$. The last two digits are $4M$.Possible values for $4M$ to be divisible by $4$ are $40, 44, 48$ (where $M$ can be $0, 4, 8$).Comparing the conditions from $(i)$ and $(ii)$,the only common value for $M$ is $8$.Therefore,$348$ is divisible by $12$ $(348 / 12 = 29)$.

For what value of $M$,is $34M$ divisible by $12$?

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