The LCM of two numbers is 12 times their HCF.  The sum of the HCF and the LCM is 403.  If one of the numbers is 93, then the other number is?

124 128 134 138

124

LCM = 12 × HCF HCF + LCM = 403 HCF + 12 HCF = 403 13 HCF = 403 HCF = 31 ∴ a × b = LCM × HCF 93 × b = 12 × 31 × 31 b = \(\frac{12 × 31 × 31}{93}\) b = 124