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(D) To find the smallest number that is divisible by $16, 24, 30$ and $32$,we first calculate the Least Common Multiple $(LCM)$ of these numbers.Prime

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$477$

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(D) To find the smallest number that is divisible by $16, 24, 30$ and $32$,we first calculate the Least Common Multiple $(LCM)$ of these numbers.Prime factorization of the numbers:$16 = 2^4$$24 = 2^3 	imes 3^1$$30 = 2^1 	imes 3^1 	imes 5^1$$32 = 2^5$$LCM = 2^5 	imes 3^1 	imes 5^1 = 32 	imes 3 	imes 5 = 480$.The number we are looking for,when increased by $3$,becomes $480$.Therefore,the required number $= 480 - 3 = 477$.

What is the smallest number which when increased by $3$ is divisible by $16, 24, 30$ and $32$?

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