Find the least number which when divided by 1 | vedclass

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(C) First,observe the difference between the divisor and the corresponding remainder:$12 - 8 = 4$$18 - 14 = 4$$36 - 32 = 4$$45 - 41 = 4$Since the diff

Vedclass · Accepted Answer

$176$

Vedclass · Answer

(C) First,observe the difference between the divisor and the corresponding remainder:$12 - 8 = 4$$18 - 14 = 4$$36 - 32 = 4$$45 - 41 = 4$Since the difference is constant $(4)$,the required number is $\operatorname{LCM}(12, 18, 36, 45) - 4$.Calculate the $\operatorname{LCM}$ of $12, 18, 36, 45$:$12 = 2^2 	imes 3$$18 = 2 	imes 3^2$$36 = 2^2 	imes 3^2$$45 = 3^2 	imes 5$$\operatorname{LCM} = 2^2 	imes 3^2 	imes 5 = 4 	imes 9 	imes 5 = 180$.Therefore,the required number $= 180 - 4 = 176$.

Find the least number which when divided by $12, 18, 36$ and $45$ leaves the remainder $8, 14, 32$ and $41$ respectively.

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