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(B) To find the smallest number which when diminished by $7$ is divisible by $12, 16, 18, 21,$ and $28,$ we first need to find the Least Common Multip

Vedclass · Accepted Answer

$1015$

Vedclass · Answer

(B) To find the smallest number which when diminished by $7$ is divisible by $12, 16, 18, 21,$ and $28,$ we first need to find the Least Common Multiple $(LCM)$ of these numbers.Step $1$: Find the prime factorization of each number:$12 = 2^2 	imes 3$$16 = 2^4$$18 = 2 	imes 3^2$$21 = 3 	imes 7$$28 = 2^2 	imes 7$Step $2$: The $LCM$ is the product of the highest powers of all prime factors present:$LCM = 2^4 	imes 3^2 	imes 7 = 16 	imes 9 	imes 7 = 1008$Step $3$: The number which when diminished by $7$ gives $1008$ is $1008 + 7 = 1015$.Therefore,the required number is $1015$.

The smallest number which when diminished by $7,$ is divisible by $12, 16, 18, 21$ and $28$ is

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