LCM( 10, 120, 180 ) = 360
Step 1 : Place the numbers inside division bar:
10 | 120 | 180 |
Step 2 : Find a prime number which can divide at least two of your numbers.
In this example we can divide by 2. If any number is not divisible by 2 write it down unchanged.
2 | 10 | 120 | 180 |
5 | 60 | 90 |
Step 3 : Repeat Step 2 until you can no longer divide.
2 | 10 | 120 | 180 |
2 | 5 | 60 | 90 |
5 | 30 | 45 |
2 | 10 | 120 | 180 |
2 | 5 | 60 | 90 |
5 | 5 | 30 | 45 |
1 | 6 | 9 |
2 | 10 | 120 | 180 |
2 | 5 | 60 | 90 |
5 | 5 | 30 | 45 |
3 | 1 | 6 | 9 |
1 | 2 | 3 |
Since there are no primes that divides at least two of given numbers, we conclude that the LCM is a product of starting numbers.
LCM = 10 · 120 · 180 = 360
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.