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(A) To find the time when the runners meet at the starting point for the first time,we need to calculate the Least Common Multiple $(L.C.M.)$ of the t

Vedclass · Accepted Answer

$1800$

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(A) To find the time when the runners meet at the starting point for the first time,we need to calculate the Least Common Multiple $(L.C.M.)$ of the time taken by each runner to complete one round.Time taken by the runners are $200$,$300$,$360$,and $450$ seconds.Prime factorization of these numbers:$200 = 2^3 	imes 5^2$$300 = 2^2 	imes 3^1 	imes 5^2$$360 = 2^3 	imes 3^2 	imes 5^1$$450 = 2^1 	imes 3^2 	imes 5^2$$L.C.M. = 2^3 	imes 3^2 	imes 5^2 = 8 	imes 9 	imes 25 = 1800$ seconds.Therefore,they will meet at the starting point after $1800$ seconds.

Four runners started running simultaneously from a point on a circular track. They took $200$ seconds,$300$ seconds,$360$ seconds,and $450$ seconds to complete one round. After how much time do they meet at the starting point for the first time? (in seconds)

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