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Find the smallest 5 digit number which is exactly divisible by 20,25 and 30.
To do: Find the smallest 5 digit number which is exactly divisible by 20,25 and 30.
Solution
To find the least 5 digit number which is exactly divisible by 20, 25 and 30, we
have to first find the LCM of 20, 25 and 30
20 = 2$\times$2$\times$5
25 = 5$\times$5
30 = 2$\times$3$\times$5
LCM = 2$\times$2$\times$3$\times$5$\times$5 = 300
So, LCM of 20, 25 and 30 is 300. But we want the least 5 digit number, which is exactly divisible by 20, 25 and 30.
Least 5 digit number = 10000.
10000 = 33$\times$300 + 100
Next higher quotient is 34.
So, the required number = 34$\times$300
= 10,200
Hence, the required number is 10,200, which is exactly divisible by 20, 25 and 30.
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