L.C.M of two numbers is 14 times their H.C.F. Sum of L.C.M and H.C.F is 900. If one of them is 120. Find the other.

Let HCF = x,

LCM = 14x

Sum of LCM and HCF = 900

$x+14x=900$

$x=60$

$HCF=60,LCM=14\times 60=840$

$\mathrm{Pr}oductoftwonumbers=LCM\times HCF$

$120\times othernumber=840\times 60$

$Othernumber=420$