LCM

Mathematics: Lowest Common Multiple (LCM)

What is LCM?

The Lowest Common Multiple (LCM) of two or more numbers is the smallest multiple that is exactly divisible by each of the numbers.

In simpler words, it’s the smallest number that appears in the multiplication tables of all the given numbers.

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Why is LCM Important?

Finding the LCM is helpful in solving problems where you need things to "line up" or "match up," such as:

• Solving fraction problems
• Scheduling events or cycles
• Determining common intervals

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Steps to Find the LCM

To find the LCM of two numbers, you can use these methods:

Method 1: Listing Multiples

1. List the multiples of each number.
2. Identify the smallest common multiple in both lists.

Example: Find the LCM of 3 and 4.

• Multiples of 3: 3, 6, 9, 12, 15, 18, …
• Multiples of 4: 4, 8, 12, 16, 20, 24, …

The smallest common multiple of 3 and 4 is 12.
So, LCM(3, 4) = 12

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Method 2: Prime Factorization

1. Write the prime factors of each number.
2. Multiply each prime factor by the greatest number of times it appears in any factorization.

Example: Find the LCM of 8 and 12.

• Prime factors of 8 = 2 x 2 x 2
• Prime factors of 12 = 2 x 2 x 3

Use the highest number of times for each prime factor:
LCM = 2 x 2 x 2 x 3

So, LCM(8, 12) = 24.

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Method 3: Division Method

1. Write the numbers in a row.
2. Divide by a common prime factor until all numbers are reduced to 1.
3. The LCM is the product of all divisors used.

Example: Find the LCM of 6 and 9.

So, LCM(6, 9) = 2 x 3 x 3 = 18

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Tips for Finding the LCM

• Use the listing method for small numbers; it’s quick and easy.
• Use prime factorization or the division method for larger numbers.

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