Question

if two positive integers P and q can be expressed as p-ab^ and q-a^b:a,b being prime numbers then LCM(P,q) are

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Answer 1

In this type of question, rewrite the numbers as a product of prime numbers.

Find the product of the greatest power of each prime factor involved in the numbers to get the HCF.

Given :

The numbers are P = ab² and Q = a³b

Step 1

$\small \bold \red{instruction}$

Rewrite the numbers as a product of prime numbers

$\small \bold \blue{calculation}$

We can rewrite a and b as

p = ab² = a × b ×

b and q = a³b = a × a × a × b The greatest powers of the prime factors are a³ and b² .

Step 2

$\small \bold \red{instruction}$

Find the product of the greatest powers of prime factors and get the LCM.

$\small \bold \blue{calculation}$

Thus, LCM = a³ × b² = a³

Hence, the LCM is a³b²

Final Answer :

LCM of p and q is

$\small\bold \blue{ = {a}^{3} {b}^{2}}$