If two positive integers p and q can be expressed asp = ab2 and q = a3b; a, b being prime numbers, then LCM (p, q) is
Question
If two positive integers p and q can be expressed asp = ab2 and q = a3b; a, b being prime numbers, then LCM (p, q) is
Solution
The least common multiple (LCM) of two numbers is the smallest number that is a multiple of both.
Given that p = ab² and q = a³b for prime numbers a and b, we can find the LCM by taking the highest powers of all primes in the numbers.
In p = ab², the powers of a and b are 1 and 2 respectively. In q = a³b, the powers of a and b are 3 and 1 respectively.
So, the highest power of a in p and q is 3, and the highest power of b is 2.
Therefore, the LCM of p and q is a³b².
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