QUESTION

CSAT

Medium

Maths

Prelims 2022

What is the smallest number greater than 1000 that when divided by any one of the numbers 6, 9, 12, 15, 18 leaves a remainder of 3?

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Explanation

The least common multiple (LCM) of 6, 9, 12, 15, and 18 is 180.

The smallest number greater than 1000 that is a multiple of 180 is 1080.

To ensure a remainder of 3 when divided by any of these numbers, we simply add 3 to 1080, resulting in:

$1080 + 3 = 1083$

Thus, the smallest number greater than 1000 that leaves a remainder of 3 when divided by any of these numbers is 1083.

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