If two positive integers p and q can be expressed as p = ab2 and q = a3b ; a, b being prime numbers, then LCM (p, q) isaba2b2a3b2a3b3
Question
If two positive integers p and q can be expressed as p = ab2 and q = a3b ; a, b being prime numbers, then LCM (p, q) isaba2b2a3b2a3b3
Solution
The LCM (Least Common Multiple) of two numbers is determined by taking the highest powers of all the prime numbers involved in the factorization of the two numbers.
Given p = ab^2 and q = a^3b, where a and b are prime numbers.
The highest power of a in both p and q is 3 (from q = a^3b) and the highest power of b in both p and q is 2 (from p = ab^2).
Therefore, the LCM of p and q is a^3b^2.
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