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?

HCF = H, LCM = 12H Sum → H + 12 H = 403 H = 31 HCF = 31 LCM = 12 × 31 H = 31 Let No’s 31x 31y LCM ⇒ 31xy = 12 × 31 ⇒ xy = 12 If (1, 12) ⇒ 1 × 31 = 31, 31 × 12 = 372 → not less than LCM If (3, 4) ⇒ 3 × 31 , 4 × 31 = 93, 124

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