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Question

Find the smallest number which when increased by 17 is exactly divisible by 520 and 468.


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Solution

Step 1: Find the LCM

Given numbers are 468 and 520

Prime factors of 468 are

468=2×2×3×3×13

Prime factors of 520 are

520=2×2×2×5×13

LCM of 468 and 520 is

LCM468,520=2×2×2×3×3×13×5=4680

Step 2: Find the smallest number.

As per given condition, the number increased by 17 is exactly divisible by 520 and 468

4680-17=4663

Hence, the number is 4663.


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