Q22 of 53 Page 1

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

Given: The numbers 468 and 520


To find: The smallest number dividing given numbers when increased by 17.


Explanation:


Calculate the LCM of the numbers to find the least number which all the given numbers divide.


Prime factorization of numbers:


468 = 2 × 2 × 3 × 3 × 13


520 = 2 × 2 × 2 × 5 × 13


LCM of given numbers = product of prime factors with highest powers


= 23 × 32 × 5 × 13


= 4680


∵ the numbers are increased by 17 to get perfect division.


We need to subtract 17 to the LCM of numbers.


∴ the least number when added by 17 gives exact division will be 4680 - 17 = 4663.


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