Mathematics often requires us to find common values between numbers, especially when working with fractions, ratios, and word problems. One of the most useful concepts is the Lowest Common Multiple (LCM). Mathematics, if not practiced, it will leave you a bit. Some are seeing finding LCM is a simple mathematic process. Yes, is true but without practice, it might be a little harder for you.
The LCM is an essential tool in arithmetic and algebra that helps simplify problems, solve equations, and even apply math in real-life situations such as scheduling, patterns, and least-time calculations.
Also Read: Understanding Fractions Made Easy
In this article, we will explain what LCM means, different methods to calculate LCM, and provide detailed examples and practice problems.
What is the Lowest Common Multiple (LCM)?
The Lowest Common Multiple (LCM) of two or more numbers is the smallest multiple that is common to all of them. That’s, a number that can divide the two numbers without any reminder. For example, if you have 4 and 6. From 4, another number that divide 4 without reminder is 8, then 12, 16 continuously. So also 6, we have 12, 18 continuously. From the two values (2, 6), and the smallest number that appear in 4 and 6 is 12. So, 12 is their LCM.
A multiple of a number is obtained by multiplying it with whole numbers.
The LCM is the first (smallest) number that appears in the list of multiples of each given number.
For example:
Find the LCM of 4 and 6.
Multiples of 4: 4, 8, 12, 16, 20, 24 …
Multiples of 6: 6, 12, 18, 24, 30 …
The smallest common multiple is 12.
So, LCM (4, 6) = 12.
Methods of Finding LCM
From the above example, we have several ways to find the Lowest Common Multiple. Depending on which one is more convenient to you.
The methods include:
1. Listing Method (Brute Force Method)
This is the simplest method where we list the multiples of each number and find the smallest common one.
Another example:
Find LCM of 5 and 7.
Multiples of 5: 5, 10, 15, 20, 25, 30, 35 …
Multiples of 7: 7, 14, 21, 28, 35, 42 …
The smallest common multiple is 35.
So, LCM (5, 7) = 35.
2. Prime Factorization Method
This method involves factorizing each number into prime numbers, then multiplying the highest powers of all prime factors.
For example:
Find LCM of 12 and 18.
- Prime factors of 12 = 22 × 3
- Prime factors of 18 = 2×32
Take the highest power of each prime:
- 22 (from 12),
- 32 (from 18).
LCM = 22 × 32 = 4 × 9 = 36.
So, LCM (12, 18) = 36.
3. Division (Short Division) Method
In this method, we divide the numbers simultaneously by prime factors until all become 1.
For example:
Find LCM of 8, 12, and 20.
Step 8 12 20
÷2 4 6 10
÷2 2 3 5
÷2 1 3 5
÷3 1 1 5
÷5 1 1 1
Multiply all divisors: 2 × 2 × 2 × 3 × 5 = 120.
So, the LCM of (8, 12, 20) = 120.
Let’s have more worked-out examples for you including word problems.
Example 1:
Find LCM of 9 and 15 using prime factorization.
9 = 32
15 = 3×5
Take highest powers: 32 × 5 = 45.
LCM (9, 15) = 45
Example 2:
Find LCM of 24, 36, and 60.
- 24 = 23 × 3
- 36 = 22 × 32
- 60 = 22 × 3 × 5
Take highest powers:
- 23 (from 24),
- 32 (from 36),
- 5 (from 60).
LCM = 23 × 32 × 5 = 360.
LCM of (24, 36, 60) = 360
Also Visit: Mastering Word Problems
Example 3:
Real-Life Application
A school bell rings every 12 minutes, and another rings every 18 minutes. If both bells ring together at 9:00 AM, when will they ring together again?
Find LCM (12, 18).
- 12 = 22 × 3
- 18 = 2 × 32
- LCM = 22 × 32 =36.
They will ring together again after 36 minutes, i.e., at 9:36 AM.
Practice Problems
Try solving these on your own:
- Find the LCM of 6 and 8.
- Find the LCM of 14, 21, and 28.
- Find the LCM of 10, 12, and 15.
- A traffic light blinks every 20 seconds, another every 30 seconds, and another every 40 seconds. If they blink together at 8:00 AM, when will they blink together again?
You Can Also Read: Fulani Tribe History
Conclusion
The Lowest Common Multiple (LCM) is a simple but powerful concept in mathematics. With different methods of finding the LCM, whether you use the listing method, prime factorization, or division method, the goal is always the same: to find the smallest number that is a multiple of all given numbers. Mastering LCM will help you in solving fraction problems, time-based questions, and many real-life scenarios. With practice, you’ll be able to find LCM quickly and confidently.