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

Solution

Let HCF = H, LCM = 12H Sum → H + 12 H = 403 or 13 H = 403 H = 31 HCF = 31  So, LCM = 12 × 31 Let no’s 31x  &  31y As we know that product of two numbers = product of HCF & product of LCM 31x × 31 y  = 31× 12 ×31  ⇒ xy = 12 We cannot take value 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 × 31 = 31, 31 × 12 = 372 → not less than LCM If values of x, yis (3, 4) ⇒ 3 × 31 , 4 × 31 = 93, 124.