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Find the smallest 4 digit number which is exactly divisible by 18, 24, 36.
Given:
18, 24 and 36.
To find:
We have to find the value of the least 4 digit number which is exactly divisible by 18, 24 and 36.
Solution:
We have to first find the LCM of 18, 24 and 36:
18 = 2 $\times$ 3 $\times$ 3
24 = 2 $\times$ 2 $\times$ 2 $\times$ 3
36 = 2 $\times$ 2 $\times$ 3 $\times$ 3
LCM = 2 $\times$ 2 $\times$ 2 $\times$ 3 $\times$ 3 = 72
So, LCM of 18, 24 and 36 is 72. But we want the least 4 digit number, which is exactly divisible by 18, 24 and 36.
Smallest 4 digit number = 1000.
Now,
1000 = (13 $\times$ 72) + 64
Next higher quotient is 14.
So, the required number = 14 $\times$ 72 = 1008
Hence, the required number is 1008, which is exactly divisible by 18, 24 and 36.
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