Question

Find LCM of P and Q if p is ABSquare and Q=a cube b where a and B are prime numbers

Answer 1

Answer:

a^xb^3

Step-by-step explanation:

Answer 2

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$\huge{\text{\underline{Solution:-}}}$

★ Given:-

p = a²b³

q = a³b

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HCF ( p,q ) = a²b

 ★ Therefore,

Product of the smallest power of each common prime factors in the numbers.

LCM ( p , q ) = a³b³

★ So, now,

Product of the greatest power of each prime factors , in the numbers.

★ Now ,

HCF ( p , q ) × LCM ( p , q )

= a²b × a³b³

= a^5b^4 → ( 1 )

Therefore, a^m × b^n = a^m + n

pq = a²b³ × a³b

     = a^5 b^4 → ( 2 ) 

from ( 1 ) and ( 2 ) , we conclude 

HCF ( p , q ) × LCM ( p ,q ) = pq

Hence proved!

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