10th Class Mathematics Real Numbers Question Bank MCQs - Real Numbers

If two positive integers p and q can be expressed as \[p=a{{b}^{2}}\]and \[q={{a}^{3}}b;\]\[a,b\] being prime numbers, then \[LCM\,(p,q)\] is: (NCERT EXEMPLAR)

A) \[ab\]

B) \[{{a}^{2}}{{b}^{2}}\]

C) \[{{a}^{3}}{{b}^{2}}\]

D) \[{{a}^{3}}{{b}^{3}}\]

Correct Answer: C

Solution :

Sol. [c] Given that, \[p=a{{b}^{2}}=a\times b\times b\]

and \[q={{a}^{3}}b=a\times a\times a\times b\]

\[\therefore \] LCM of p and \[q=LCM(a{{b}^{2}},{{a}^{3}}b)\]

\[=a\times b\times b\times a\times a={{a}^{3}}{{b}^{2}}\]