If two positive integers p and q can be expressed as p=ab^ 2 \& q = a ^ 3 * b where a, b being prime numbers then LCM (p, q) is equal to a. ab b. a ^ 2 * b ^ 2 c. a ^ 3 * b ^ 2 d. a ^ 2 * b ^ 3
Question
If two positive integers p and q can be expressed as p=ab^ 2 & q = a ^ 3 * b where a, b being prime numbers then LCM (p, q) is equal to a. ab b. a ^ 2 * b ^ 2 c. a ^ 3 * b ^ 2 d. a ^ 2 * b ^ 3
Solution
The LCM (Least Common Multiple) of two numbers is the smallest number that is a multiple of both.
Given that p = ab^2 and q = a^3b, we need to find the LCM of p and q.
The LCM of two numbers is found by multiplying the highest powers of all the primes appearing in the numbers.
In p = ab^2, the highest power of a is 1 and the highest power of b is 2.
In q = a^3b, the highest power of a is 3 and the highest power of b is 1.
So, the LCM of p and q will be a^3b^2.
Therefore, the answer is c. a^3b^2.
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