The LCM of the two numbers is 12 times their HCF. The

Solution

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.