The LCM of two numbers is 20 times their HCF, and the sum of the LCM and the HCF is 504. If the difference of the numbers is 24, then find the sum of the numbers.

Explanation

Let the HCF =x then, LCM=20x ATQ-20x+x =504 21x =504 X =24. LCM=480 HCF=24 Hence, the product of HCF and LCM = 480 × 24 = 11520 Let the numbers be P and Q (P > Q). Hence, PQ = 11520 According to the question, P - Q = 24 (P - Q)2=242 (P - Q) + 4PQ = 24 + 4PQ (Adding 4PQ on both side) (P - Q) + 4PQ = 24 + 4 × 11520 ( ∵ PQ = 11520) (P + Q)2 = 46656 (P + Q) = 216