The LCM of the two numbers is 12 times their HCF. The sum of LCM and HCF is 429 and if both the number are smaller than their
LCM. Find both numbers.

LCM =12 HCF LCM: HCF = 12:1 ATQ-       13 = 429 1 = 33 HCF = 33 LCM = 33×12 = 396 Let the no 33x and 33y. As we know the product of two numbers = product of HCF & product of LCM 33x ×33y = 33 ×33×12 x y = 12 We cannot take values of x & y = 2 & 6 because these have 2 in common extra but there must be nothing common as 12 HCF is already taken. If values of x, y is (1, 12) ⇒ 1 × 33 = 33, 33 × 12 = 396 → not less than LCM If values of x, y is (3, 4) ⇒ 3 × 33, 4 × 33 = 99, 132.