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Question
Find the least 5-digit number which is exactly divisible by 20, 25 and 30.
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Solution
20 = 1 × 2 × 2 × 5 = 22 × 51
25 = 1 × 5 × 5 × 31 = 52
30 = 1 × 2 × 3 × 5 = 21 × 31 × 51
LCM of 20, 25 and 30 = 22 × 31 × 52 = 300
Least five digit number is 10000
Now, if we divide 10000 by 60, we will get 33.33 as quotient.
The integer just greater than 33.33 is 34
∴ Required number = 300 × 34 = 10200
Hence, the least 5-digit number which is exactly divisible by 20, 25, 30 is 10200.
25 = 1 × 5 × 5 × 31 = 52
30 = 1 × 2 × 3 × 5 = 21 × 31 × 51
LCM of 20, 25 and 30 = 22 × 31 × 52 = 300
Least five digit number is 10000
Now, if we divide 10000 by 60, we will get 33.33 as quotient.
The integer just greater than 33.33 is 34
∴ Required number = 300 × 34 = 10200
Hence, the least 5-digit number which is exactly divisible by 20, 25, 30 is 10200.
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