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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,
2 | 16,18,24,30 |
2 | 8,9,12,15 |
2 | 4,9,6,15 |
3 | 2,9,3,15 |
2 | 2,3,1,5 |
3 | 1,3,1,5 |
1,1,1,5 |
$LCM=2\times 2\times 2\times 2\times 3\times 3\times 5=2^{4} \times 3^{2} \times 5=16\times 9\times 5=144\times 5=720$
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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