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