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

Let LCM = m, HCF = n,
According to the question,
m = 12n, .......(i)
and m + n = 403.......(ii)
⇒ 12n + n = 403 [from Eq.(i)]
⇒ 13n = 403
∴ n = 403/13 = 31
∴ m = 12 x 31 = 372
Let the another number = k
∴ 93 x k = 372 x 31
[as product of two numbers HCF x LCM]
⇒ k = (372 x 31)/93 = 124