Q) Write the smallest number which is divisible by both 306 and 657.

Ans:

(Note: Here, it is important to understand that since we need to find a number which is divisible by given 2 numbers, then it has to be a multiple of these given numbers, not a factor. Why? Because, factor will always be smaller than the numbers and will not be divisible by the numbers)

By prime factorisation, we get:

306 = 3 x 3 x 2 x 17

657 = 3 x 3 x 73

∴ LCM = Common multiples x uncommon multiples = (3 x 3) x (2 x 17) x (73) = 22,338

Therefore, the smallest number divisible by 306 and 657 is 22, 338.

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