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

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 $a^{3} b^{2}$
Given,
$p = a b^{2} = a \times b \times b$
$q = a^{3} b = a \times a \times a \times b$
L.C.M of $p, q$ is $a^{3} b^{2}$

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

Q. 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

Q. If p and q are positive integers such that p = ab² and q = a³b, where a, b are prime numbers, then LCM (p, q) = ?

(a) ab
(b) a²b²
(c) a³b²
(d) a³b³

Q. If two positive integers

p

and

q

are written as

p = a^{2} b^{2}

and

q = a^{3} b

, a,b are prime numbers then verify that

L . C . M . (p, q) \times H . C . F . (p, q) = p q

If two positive integers P and Q are written as P=A² B³and Q=A³b, A, B are prime numbers, then Verify LCM (p,q)× HCF (p, q) =pq ?

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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

The correct option is C a3b2Given,p=ab2=a×b×bq=a3b=a×a×a×bL.C.M of p,q is a3b2

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

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