Question

If p and q are positive integers such that p = ab^2 and q = a^3b where a and b are prime. Numbers. Then. Find their lcm

Answer 1

Answer:

A^{3} B^{2}

explanation:

P =  A* B* B

Q = A*A*A*B

LCM OF P AND Q = LCM OF$B^{2} A, A^{3} B$= a*b*b*a*a = $a^{3} b^{2}$

[ lcm is the product of the greatest power of each prime factor ]

Answer 2

The lcm of p and q is  $a^3b^2$ .

Explanation:

We are given that ,  p and q are positive integers such that p = ab²and q = a³b  , where a and b are prime.

Then ,the prime factorization of p is $a\times b\times b$

The prime factorization of q is  $a\times a\times a\times b$

• The lcm of two numbers m and n is the least number that is divisible by both ma nd n.

The lcm of p and q is $lcm(p,q)=a\times a\times a\times b\times b= a^3b^2$

Therefore , the lcm of p and q is  $a^3b^2$ .

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