Find the smallest 4 digit number which is exactly divisible by 72 and 108with explaination

Mathematics

1 answer:

likoan [24]1 year ago

5 0

The smallest 4-digit number which is exactly divisible by 72 and 108 is 1080.

The least common multiple that is divisible by both a and b is the smallest positive integer, lowest common multiple, or smallest common multiple of two numbers a and b, generally indicated by LCM.

The Least common multiple of both the numbers 72 and 108 is 216. Since 216 is the least common multiple of both the numbers. Therefore, the four-digit number needs to be a multiple of 216 to be divisible by both the numbers. Thus, when 216 is multiplied by 5 the result is 1080, which is divisible by both 72 and 108. Hence, the smallest 4-digit number which is exactly divisible by 72 and 108 is 1080.

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