Question

Two positive integers 'p' and 'q' can be expressed as p = a * b ^ 2 and q = a ^ 2 * b are prime numbers. What is the L.C.M of 'p' and 'q'

Answer 1

For finding LCM of some numbers, we take highest power of the prime factors involved in the numbers.

Here

p = ab²

q = a²b

Highest power of a is in q, that is 2 (a²)

Highest power of b is in p, that is also 2 (b²)

Hence, the LCM(p, q) will be = a²b²

(Multiplying the highest powers of each factor gives LCM)

Answer 2

Given :-

Two positive integers 'p' and 'q' can be expressed as p = ab² and q = a²b

are  prime numbers.

To Find :-

LCM

Solution :-

p and q are positive number and as well as prime

p = ab² = a × b × b

q = a²b = a × a × b

LCM = (a × a × b × b)

LCM = a² × b²

LCM = a²b²