the H.C.Of two numbers is 7and their L.C.M is 140.If one of the numbers is 28,find the other number

2 answers

the two numbers are 7a and 7b
where a & b have no common factors
The LCM is ab/7
So, if 7a=28, 28b/7 = 140
b = 140*7/28 = 20/4 = 5
check: LCM(28,35) = 140
140 = 2*2*5*7
28 = 2*2*7

140/28 = 35 , both 140 and 28 have a factor of 7, but not the 5
So it looks like 35 is the other number.

check:
35 = 5*7
28 = 4*7

Highest common factor is 7
LCM = 5*7*4 = 140