Find the smallest 5 digit number which is exactly divisible by 16, 18, 24 and 30.

Given :

The  smallest 5 digit number which is exactly divisible by 16, 18, 24 and 30.

To find :

We have to find the smallest 5 digit number which is exactly divisible by 16, 18, 24 and 30.

Solution :

The smallest 5 digit number which is exactly divisible by 16, 18, 24 and 30 is a multiple of the LCM of the given numbers.

LCM of 16, 18, 24 and 30 is,

$LCM=2\times 2\times 2\times 2\times 3\times 3\times 5=2^{4} \times 3^{2} \times 5=16\times 9\times 5=144\times 5=720$

Multiples of 720 are $720\times1=720,720\times2=1440,....720\times14=10080$

Therefore, the smallest 5 digit number which is exactly divisible by 16, 18, 24 and 30 is 10080.

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Updated on: 10-Oct-2022

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