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Q.

The least 5-digit number that is exactly divisible by 20, 25 and 30 is ____.


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Detailed Solution

The least 5-digit number that is exactly divisible by 20, 25 and 30 is 10,200.
We have been given the numbers 20, 25 and 30.
Calculating the LCM of 20, 25, and 30,
20=1×2×2×5=( 2 2 )×( 5 1 )  
25=1×5×5×31= 5 2  
30=1×2×3×5  
Common factors are,
⇒2×3×5×5=300
The LCM of 20, 25 and 30 is 300.
We know, the least 5-digit number is 10000.
Let’s divide 10000 by 300,
We get a 33.33 quotient.
And the closest greater integer to 33.33 is 34.
Therefore, the required number is,
300×34=10200  
Therefore, the correct answer is 10,200.
 
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