Q3/014) The ratio of L.C.M & H.C.F of two numbers is 6:1 and the smallest number is 12, then find the larger number?

let LCM = a and HCF = b

for 2 numbers product of number = product of LCM and HCF

let larger number be l

12l = ab
and a = 6b or 6b^2 = 12l or b^2 = 2l

b is a factor of 12 but not 12 ( it is 1 or 2 or 3 or 4 or 6) and l >12 => b^2 > = 24 so b = 6 and l = 18