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Question

Find the least number of five digits that is exactly divisible by 16, 18, 24 and 30.

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Solution

LCM of 16, 18, 24 and 30:

216,18,24,3028,9,12,1524,9,6,1522,9,3,1531,9,3,1531,3,1,551,1,1,51,1,1,1

LCM = 24 × 32 × 5 = 720

We have to find the least five-digit number that is exactly divisible by 16, 18, 24 and 30.
But LCM=720 is a three digit number.

The least five digit number = 10000
Dividing 10000 by 720
, we get:
7201310000-7202800-2160640The greatest four-digit number exactly divisible by 720 = 10000-640=9360So, the least five-digit number exactly divisible by 720 = 9360 + 720= 10080

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