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Prime Factorization and LCM of Two Numbers

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Question

Two boys start jogging together on a circular track. If they respectively take 30 minutes and 20 minutes to complete one round, when will they meet ?

A

after 50 minutes

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B

after 60 minutes

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C

after 40 minutes

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D

after 90 minutes

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Solution

The correct option is B after 60 minutes
Prime Factorisation of 30 = 2 x 3 x 5
Prime Factorisation of 20 = 2 x 2 x 5
Least common multiple of 20 & 30 is 2 x 2 x 3 x 5 = 60 minutes
$∴$ Both boys will meet after 60 minutes.

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