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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Solution

The answer is C.
Given that, $p = a b^{2} = a \times b \times b$
$q = a^{3} b = a \times a \times a \times b$

LCM is the product of the greatest power of each prime factor involved in the numbers

$∴$ LCM of p and q = LCM $(a b^{2}, a^{3} b) = a \times a \times a \times b \times b = a^{3} b^{2}$

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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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Question 7 If two positive integers p and q can be expressed as p = ab2 and q=a3b; where a, b being prime numbers, then LCM (p, q) is equal to A) ab B) a2b2 C) a3b2 D) a3b3

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

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) $a^{3} b^{3}$

The answer is C.
Given that, $p = a b^{2} = a \times b \times b$
$q = a^{3} b = a \times a \times a \times b$

LCM is the product of the greatest power of each prime factor involved in the numbers

$∴$ LCM of p and q = LCM $(a b^{2}, a^{3} b) = a \times a \times a \times b \times b = a^{3} b^{2}$