Find the smallest 4 digit number that is exactly divisible by 36, 40, and 45.

Given :

The given numbers are 36, 40, 45.

To do :

We have to find the smallest 4 digit number that is exactly divisible by 36, 40, and 45.

Solution :

The smallest 4 digit number which is divisible by 36, 40, and 45 will be a multiple of their LCM.

Therefore,

LCM of 36,40 and 45 is,

$36=2\times 2\times 3\times 3$

$40=2\times 2\times 2\times 5$

$45=3\times 3\times 5$

LCM of 36, 40 and 45 $=  2\times 2\times 2\times 3\times 3\times 5 = 8 \times 9 \times 5 = 360$

Required smallest 4 digit number which is divisible by 36, 40, and 45 is a multiple of 360.

Multiples of 360 are 360, 720, 1080,...

The smallest 4 digit number that is exactly divisible by 36,40 and 45 is 1080.

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Updated on: 10-Oct-2022

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