Q8 of 124 Page 1

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

To find the smallest number we should find LCM of 468 and 520


Prime factors of 468 = 2 × 2 × 3 × 3 × 13


Prime factors of 520 = 2 × 2 × 2 × 5 × 13


Hence LCM of 468 and 520 = 2 × 2 ×2 × 3 × 3 ×5×13 = 4680


Therefore the smallest number which when increased by 17 is exactly divisible by both 520 and 468= LCM – 17 ⇒ 4680 – 17 = 4663


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