If two positive integers p and q can be expressed as $p = a b^{2}$ and $q = a^{3} b$ . The numbers $a, b$ are prime numbers. Then, the LCM of $p$ and $q$ is

a b

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a^{2} b^{2}

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a^{3} b^{2}

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a^{3} b^{3}

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Solution

The correct option is C $a^{3} b^{2}$
Factors of $p = a \times b \times b$
Factors of $q = a \times a \times a \times b$
Therefore, L.C.M. of $p$ and $q$ is $= a \times b \times b \times a \times a$
$= a^{3} b^{2}$

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Question 7
If two positive integers p and q can be expressed as p = $a b^{2} a n d q = a^{3} b$ ; where a, b being prime numbers, then LCM (p, q) is equal to

A) $a b$
B) $a^{2} b^{2}$
C) $a^{3} b^{2}$
D) $a^{3} b^{3}$

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p

and

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and

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If two positive integers p and q can be expressed as p=ab2 and q=a3b . The numbers a,b are prime numbers. Then, the LCM of p and q is

The correct option is C a3b2Factors of p=a×b×bFactors of q=a×a×a×bTherefore, L.C.M. of p and q is =a×b×b×a×a =a3b2

If two positive integers p and q can be expressed as $p = a b^{2}$ and $q = a^{3} b$ . The numbers $a, b$ are prime numbers. Then, the LCM of $p$ and $q$ is

The correct option is C $a^{3} b^{2}$
Factors of $p = a \times b \times b$
Factors of $q = a \times a \times a \times b$
Therefore, L.C.M. of $p$ and $q$ is $= a \times b \times b \times a \times a$
$= a^{3} b^{2}$