Question

Sum of two positive integers is 52 and their LCM is 168. Find the numbers.

Answer 1

52=4*13; 168=4*6*7 So HCF=4

Let the numbers be 4a and 4b

4a+4b=52; a+b=13

4ab=168; ab=42

a-b=square root of {(a+b)^2–4ab}=of{169–168}=of 1

=plus or minus 1

So a=6 and b=7;

The numbers are 24 and 28