How To Find The Lcm Of Two Or More Integers – Step-By-Step Guide

Least Common Multiple

The smallest multiple (other than zero) that two or more numbers have in common.

The least common multiple (LCM) of two or more integers is the smallest positive integer that is a multiple of each of the given integers. LCM can be found by finding the prime factors of each number and expressing each number as a product of its prime factors.

To find the LCM of two or more integers, the following steps can be followed:

Step 1: Prime factorize each integer.
For example, let’s find the LCM of 12 and 18.
12 = 2^2 * 3
18 = 2 * 3^2

Step 2: Write down the factors from each number, including their highest powers.
The factors of 12 are 2^2 and 3. The factors of 18 are 2 and 3^2. The highest powers are 2^2 and 3^2.

Step 3: Multiply the factors together.
2^2 x 3^2 = 36

Step 4: Simplify, if necessary
The LCM of 12 and 18 is 36.

It is important to note that the LCM of any set of integers can also be found using the greatest common factor (GCF) of the integers. The formula for finding the LCM of two integers using the GCF is LCM(a,b) = (a * b) / GCF(a,b).

In summary, to find the LCM of any set of integers, first prime factorize each integer, write down the factors with their highest powers, multiply these factors together, and if necessary simplify the result.

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