Question

If a and b are relatively coprime numbers , then prove that lcm of ma and mb is mab

Answer 1

Given that a and b are coprime. Thus the LCM of a and b is ab. Now LCM of m and m is of course m.
Thus, the LCM of ma and mb is m×ab= mab

Answer 2

Answer: Proved.

Step-by-step explanation:  Given that 'a' and 'b' are relatively prime. We are given to prove that the lcm of ma and mb is mab.

We know that the lcm of two co-prime numbers is equal to the product of the two numbers.

So, the lcm of 'a' and 'b' will be

$lcm(a,b)=a\times b=ab.$

Since 'm' is present in both the numbers 'ma' and 'mb', so in the lcm of 'ma' and 'mb', we will multiply 'm'.

Thus, the lcm of 'ma' and 'mb' is 'mab'.