How to find the LCM of two numbers m and n without using factorization?

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter5: Factoring Polynomials
Section5.3: Monomials Factors Of Polynomials
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How to find the LCM of two numbers m and n without using factorization?

Expert Solution
Step 1

LCM is the least common factor of two or more numbers.

Step 2

Let HCF of (a,b) =p and LCM( a,b) = q

So, a=pr and b=ps where r and s have no common factors.

Then, a s =p r s ….(1)

b r = p r s …..(2)

Step 3

The greatest factor in the product r s will be 1.

p r s= LCM of (a,b)

p r s=q ….(3)

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