Online Least Common Multiple Calculator
How to use the Least Common Multiple Calculator?
Follow the steps below to use the Least Common Multiple calculator:
Step 1: Enter the known numbers into the respective input box and their least common multiple will be calculated.
Step 2: Click on the ‘Solve’ button to obtain the result.
Step 3: Click on the ‘Show Steps’ button to view the stepwise solution applied to find the least common multiple.
Step 4: You can also select a method of calculation from the dropdown box.
Step 5: Click on the 
button to enter new inputs and start again.
Step 6: Click on the ‘Example’ button to play with different random input values.
Step 7: Click on the ‘Explore’ button to understand how to find the lowest common multiple using the method of listing multiples.
Step 8: When on the ‘Explore’ page, click the ‘Calculate’ button, if you want to go back to the calculator.
What are Least Common Multiples?
The least common multiple of two or more numbers is the smallest ‘nonzero’ multiple that is common among these numbers. The term least common multiple is often abbreviated as LCM.
Methods used in the Least Common Multiple Calculator
Different methods can be used to find the LCM. Let’s learn about two such methods.
- Listing multiples
First, we multiply the given numbers by natural numbers starting from 1, 2, 3, and so on, to find consecutive multiples of the numbers. Then we list down these multiples in ascending order. The common multiples among these numbers are noted. The smallest common multiple is the LCM of the given numbers.
- Prime Factorization
In this method the prime factorization of the given numbers is found. Then, factors that are common among at least two of the given numbers are grouped. From one group of like factors, only one prime factor is considered. Then each of these factors are multiplied by the remaining ungrouped prime factors. The product of these factors will be LCM of the given numbers.
Solved Examples
Example 1: Find the least common multiple of 5, 8 and 10 by listing their multiples.
Solution:
Multiples of 5 : 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, . . .
Multiples of 8 : 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, . . .
Multiples of 10 : 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, . . .
The common multiples are 40, 80, 120, . . .
Hence, the least common multiple of 5, 8 and 10 is 40.
Example 2: Find the least common multiple of 12, 15 and 20 using prime factorization.
Solution:
The factor tree of 12, 15 and 20 can be drawn as in the images.
Prime factorization of 12 : 2 \(\times\) 2 \(\times\) 3
Prime factorization of 15 : 3 \(\times\) 5
Prime factorization of 20 : 2 \(\times\) 2 \(\times\) 5
LCM : 2 \(\times\) 2 \(\times\) 3 \(\times\) 5 = 60
Hence, the least common multiple of 12, 15 and 20 is 60.
Example 3: John and Tom are running on a track. John completes one lap in 5 minutes and Tom completes it in 7 minutes. If they start together, after how long will they meet again at the starting point?
Solution:
John and Tom take 5 minutes and 7 minutes respectively to complete one lap. To calculate the time taken to meet at the starting point, we need to find the LCM of 5 and 7.
Multiples of 5 : 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, . . .
Multiples of 7 : 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, . . .
The common multiples of 5 and 7 are 35, 70, 105 . . .
So, the LCM of 5 and 7 is 35.
Hence, John and Tom will meet again at the starting point after 35 minutes.
The greatest common factor or GCF is the largest number that is divisible by all the given numbers. The least common multiple or LCM is the smallest number that is a common multiple of the given numbers. For example, for 12 and 24, the GCF is 12 and the LCM is 24.
When a number is multiplied by any natural number the product obtained is a multiple of the given number.
Co-prime numbers are numbers that have no common factors, other than 1 between each other. Therefore, the least common multiple of two co-prime numbers is the product of the two numbers.
Multiples that follow each other continuously in increasing order. For instance, the first three consecutive multiples of 9 are 9, 18 and 27.