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Question

Find the least number that is divisible by all the numbers between 1 and 10 (both inclusive).

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Solution

The least number that is divisible by
(1,2,3,4,5,6,7,8,9,10)
we have to take LCM of given numbers.
As all number are divisible by 1, than
we neglect if
using prime factors
2=2, 3=3, 4=2×2, 5=5
6=2×3, 7=7, 8=2×2×2, 9=3×3, 10=2×5
Now LCM of given number is =2×2×2×3×3×5×7×
=8×9×35
LCM=2520
2520 is least number divisible by (1.....10) both inclusive.

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