The LCM of two numbers is 12 times their HCF. The sum of LCM and HCF is 403 and if both the number are smaller than their
LCM. Find both the numbers?

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.