Question

7. If two positive integers p and q can be
expressed as p = ab2 and q = a b, a, b being
prime numbers, then LCM (p, q) is
NEXT
(A) ab
(B) a2b2
(C) a3b2
(D) a3b3​

Answer 1

Answer:

C)a³b³

Step-by-step explanation:

Given that, p = ab2 = a × b × b

Given that, p = ab2 = a × b × band q = a3b = a × a × a × b

Given that, p = ab2 = a × b × band q = a3b = a × a × a × b∴ LCM of p and q = LCM (ab2,a3b) = a × b × b × a × a = a3b2

Given that, p = ab2 = a × b × band q = a3b = a × a × a × b∴ LCM of p and q = LCM (ab2,a3b) = a × b × b × a × a = a3b2[Since, LCM is the product of the greatest power of each prime factor involved in the numbers].