hcf & lcm 文字題

let the two number is a,b
then since hcf of 2 numbers is 14 , we can make
a=14m
b=14n
where m and n are coprime
lcm of 2 numbers is 168
that is [14m,14n]=168
14[m,n]=168
[m,n]=12
Now, we know m and n are coprime and lcm of m,n is 12
12=2*2*3
So the only possibility is
m=4, n=3 or m=3, n=4
Without loss of generality
let m=4, n=3 ,then a=56, b=42
their sum
a+b
=56+42
=98