Question

The LCM of two numbers is 2900% more than their HCF and sum of LCM and HCF of two number is 310. If one of the number is 20, find the other number. A. 300 B. 75 C. 290 D. 150

Answer 1

Let H.C.F of two numbers be 'x'.
Given that L.C.M is 2900% more than L.C.M
Therefore,
L.C.M=x+2900/100×x
LCM=x=29x=30x.....................1
as per goven condition we have,
LCM+HCF=310
30x+x=310
x=10
HCF of two numbers =10
Then, LCM of two numbers=30×10=300
We know that,
LCM×HCF=a×b
300×10=20×b
300×10/20=b
b=150
Hence,
LCM of two numbers=300
HCF of two numbers=10
Two numbers=20 and 150
i.e another number is 150.