Question

HCF and LCM of two numbers are same. Find the difference between two numbers.​

Answer 1

HCF and LCM of two numbers can be same only if two numbers are equal. Hence their difference will be zero.

Let a and b two positive integers. Then gcd(a,b) is a common divisor of a and b and therefore gcd(a,b)≤min(a,b). On the other hand lcm(a,b) is a common multiple of a and b and therefore lcm(a,b)≥max(a,b). Hence

gcd(a,b)≤min(a,b)≤max(a,b)≤lcm(a,b)

(gcd is the same of hcf). So if gcd(a,b)=lcm(a,b) then min(a,b)=max(a,b), that is a=b.