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Mathematics

Find the least number which when divided by 24, 36, 45 and 54 leaves a remainder of 3 in each case.

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Answer

First, we find the LCM of 24, 36, 45 and 54.

224, 36, 45, 54
212, 18, 45, 27
26, 9, 45, 27
33, 9, 45, 27
31, 3, 15, 9
31, 1, 5, 3
51, 1, 5, 1
1, 1, 1, 1

LCM of 24, 36, 45 and 54 = 2 × 2 × 2 × 3 × 3 × 3 × 5 = 1080.

The required least number which leaves remainder 3 = 1080 + 3 = 1083.

Hence, the required least number is 1083.

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