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  • If two positive integers p and q can be expressed as p = absq2 and q = acub3b; a,bbeing prime numbers then LCM (p, q) is (A) ab(B) asq2bsq2(C) acube3bsq2(D) acube3bcube3

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) is

        (A) ab              (B) a2b2                        (C) a3b2                        (D) a3b3

Answers (1)

Answer.  [C]
Solution.        
p= ab^{2}= a\times b\times b
q= a^{3}b= a\times a\times a\times b
For LCM, we have to take all the primes from prime factorization of two number.
The common prime in both numbers has to be taken only once.
Therefore,
\text{LCM =}a\times a\times a\times b\times b= a^{3}b^{2}
Hence option C is correct.

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