Question

if two positive integers A and B are expressible in the form of a =pq^2 and b = p^3 q ; p, q being prime numbers then LCM of (a,b) is​

Answer 1

LCM(a,b) = product of highest exponent of common factors
common factors of a and b are p and q
therefore, LCM(a,b) =pcube *q square

Answer 2

The LCM of (a,b) is​ $p^3q^2$.

Step-by-step explanation:

The given numbers are

$A=pq^2$

$B=p^3q$

p, q being prime numbers.

Factor form of given numbers are

$A=p\times q\times q$

$B=p\times p\times p\times q$

The LCM of a and b is

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

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

Therefore, the LCM of (a,b) is​ $p^3q^2$.

#Learn more

If two positive integers 'a' and 'b' are expressible in the form a =pq^2, b=p^2q,p,q are prime numbers then show that LCM (a,b)×HCF(a,b)=a×b.

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