There are two numbers a and b whose product is 192 and the quotient of AM by HM of their greatest common divisor and least common multiple is `(169)/(48). The smaller of a and b is

Options

A. 2
B. 4
C. 6
D. 12

Answer

B, D

Explanation

If G=GED of a and b,L=LCM of a and b, we have `GL=ab=192 " " "……(i)"`
`(AM)/(HM)` of G and L is `((G+L)/(2))((G+L)/(2GL))=(169)/(48)`
`implies (G+L)^(2)=(169)/(12)GL=(169)/(12)GLxx192=13^(2)*4^(2)`
`G+L=52` but `GL=192`
`implies G=4,L=48 implies a=4,b=48` or `a=12,b=16`