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Quick LCM Calculator - Find Common Multiple in Seconds

Anand Pal

Anand Pal

— 5 min read

The Least Common Multiple (LCM) is also known as the Lowest Common Multiple (LCM) which is one of the most important methods in math, especially in number theory.

The LCM of two numbers can be the smallest number that can be divided equally by both a and b, and that is written as LCM(a, b).

— Checkout few examples of LCM:

  • LCM(2, 3) = 6
  • LCM(6, 10) = 30

Overall you can uderstand that the LCM can be found for two or more than two numbers. It is the smallest number that can be divided by all the numbers in the set.

That's how simple LCM is 😄

Number of ways to find LCM

You can find LCM in many different ways. Here are the 5 different ways you can use to find LCM. It's on you which approach you will take.

1. Listing Multiples Method

  • Write down the multiples of each number until all the number in the list share at least one multiple.
  • Find the smallest number that are common in all of the groups.

Checkout real life example for calculating LCM using Listing Multiples methods.

Find LCM(6, 9, 15)

Multiples of 6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102

Multiples of 9 = 9, 18, 27, 36, 45, 54, 63, 72, 81, 90

Multiples of 15 = 5, 30, 45, 60, 75, 90, 105, 120, 135, 150

Here is the answer for LCM(6, 9, 15) = 90.

90 is the smallest common multiple of 6, 9, and 15.

2. Prime Factorization Method

  • You have to first find the prime factors of each number.
  • Make the list of all the prime factors and take the highest number from each factor and multiply them together.

Checkout real life example for calculating LCM using Prime Factorization Method

Find the LCM(3, 5, 9)

Step 1: Break down each number into prime factors.

  • 3 is a prime number, so it stays 3.
  • 5 is also a prime number, so it stays 5.
  • 9 can be broken down into 3 × 3

Step 2: List all the factors.

  • We have: 3, 5, and 3 × 3.

Step 3: Take the highest number of each factor.

  • We have 3 and 5.
  • We need two 3s (from 9) and one 5.

Step 4: Multiply them all together.

  • Now, we multiply: 3 × 3 × 5 = 45.
So, the answer for the LCM (3, 5, 9) = 45!

3. Cake/Ladder Method

  • List the numbers in a row and divide them by any prime number that can split at least two of the numbers.
  • Keep splitting until you can't divide any more further.

Checkout example for calculating LCM using Ladder Method

Find the LCM(4, 7, 12)

Step 1: First write the numbers in a row

  • 4, 7, 12

Step 2: Divide by 2 (the smallest prime number) because 4 and 12 are even.

  • 2 | 4, 7, 12
  •    | 2, 7, 6

Step 3: Divide by 2 again, because 2 is even.

  • 2 | 2, 7, 6
  •    | 1, 7, 3

Step 4: Divide by 3, because 3 divides with 3.

  • 3 | 1, 7, 3
  •    | 1, 7, 1

Now we’re done because we left 1 at the end of the division. Multiply all the numbers that we have used to divide: 2 × 2 × 3 × 7 = 84

So, the answer for the LCM (4, 7, 12) = 84!

4. Division Method

  • Line up the numbers and divide them by the smallest prime number that splits at least one of them.
  • Do this again and again until all the numbers are lowered to 1.
  • The LCM is the sum of the prime numbers that are used to divide the numbers.

Checkout example for calculating LCM using Division Method

Find the LCM(12, 18, 21)

Step 1: First write the numbers in a row

  • 12, 18, 21

Step 2: Divide by 2 (the smallest prime number)

  • 2 | 12, 18, 21
  •    | 6, 9, 21

Step 3: Divide by 2 again, because 6 can be divided by 2.

  • 2 | 12, 18, 21
  • 2 | 6, 9, 21
  •    | 3, 9, 21

Step 4: Divide by 3, because 3 can be divided by each number.

  • 2 | 12, 18, 21
  • 2 | 6, 9, 21
  • 3 | 3, 9, 21
  •    | 1, 3, 7

Step 5: Divide by 3, because 3 can be 3.

  • 2 | 12, 18, 21
  • 2 | 6, 9, 21
  • 3 | 3, 9, 21
  • 3 | 1, 3, 7
  •    | 1, 1, 7

Step 6: Divide by 7 because 7 can be divided with 7.

  • 2 | 12, 18, 21
  • 2 | 6, 9, 21
  • 3 | 3, 9, 21
  • 3 | 1, 3, 7
  • 7 | 1, 1, 7
  •    | 1, 1, 1

Now we’re done because we left 1 at the end of the division. Multiply all the numbers that we have used to divide: 2 × 2 × 3 x 3 × 7 = 252

So, the answer for the LCM (12, 18, 21) = 252!

Conclusion

There are different ways to find the LCM, you can choose one that works best for you. Learning these methods improves your ability to solve math problems and gives you an idea of how to solve them without using any calculator.

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