Question

The HCF of two numbers is 1/28 of their LCM, and the sum of the LCM and the HCF is 116. If one of the number is 16. Find the other.

Answer 1

Dear Student,
Sol :
Given H.C.F (a,b) = 1/28 L.C.M (a,b)
And H.C.F (a,b) + L.C.M (a,b) = 116 then
1/28 L.C.M (a,b) + L.C.M (a,b) = 116
L.C.M (a,b) [ 1 + 1/28 ] = 116
L.C.M (a,b) = 112 then H.C.F (a,b) = 4
But we know that a = 16 .
a x b = H.C.F (a,b) x L.C.M (a,b)
b = (112 x 4) / 16 = 28
∴ other num is 28.
Regards