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7. If two positive integers p and q can beexpressed as p = ab2 and q = a b, a, b beingprime numbers, then LCM (p, q) isNEXT(A) ab(B) a2b2(C) a3b2(D) a3b3 |
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Answer» 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]. |
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