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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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