Question

If two positive integers p and q can be expressed as p=ab2 and q=a3b where a,b being prime numbers then LCM PQ is

Answer 1

P=ab^2 Q=a^3b

FACTORS OF P(ab^2)= a×b×b

FACTORS OF Q(a^3b)= a×a×a×b

so,LCM OF PQ= a×a×a×b×b

= a3b2

Answer 2

The LCM of pq is $a^3b^2$.

Step-by-step explanation:

Given : If two positive integers p and q can be expressed as $p=ab^2$ and $q=a^3b$ where a,b being prime numbers.

To find : The LCM of pq ?

Solution :

Factoring the numbers,

$p=ab^2=a\times b\times b$

$q=a^3b=a\times a\times a\times b$

The LCM is the least common multiple,

$LCM(ab^2,a^3b)=a\times a\times a\times b\times b$

$LCM(p,q)=a^3\times b^2$

$LCM(p,q)=a^3b^2$

Therefore, the LCM of pq is $a^3b^2$.

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