Question

on a morning walk three persons step off together and their steps measure 40 cm 42 cm and 45cm respectively what is the minimum distance each should walk so that each can cover the same distance in complete steps​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

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$\green{\underline \bold{Given :}}$

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• Measure of steps are 40cm , 42cm & 45cm.

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$\red{\underline \bold{To \: Find:}}$

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• Minimum distance each should walk so that each can cover the same distance in complete steps.

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$\large{\orange{\underline{\tt{Solution :-}}}}$

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The minimum distance covered by each of them in complete steps = LCM of the measures of their steps

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⇛ $\sf LCM(40 , 42 , 45)$

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៚ $\sf 40 = 2 × 2 × 2 × 5 = 2^3 × 5$

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៚ $\sf 42 = 2 × 3 × 7$

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៚ $\sf 45 = 3 × 3 × 5 = 3^2 × 5$

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$\sf \dashrightarrow LCM(40 , 42 , 45) = 2^3 ×3^2 × 5 × 7 = 2520$

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᪣ Each person should walk a minimum distance of 2520 cm in complete steps.

$\rule{200}5$