LCM( 200, 400, 900 ) = 3600
Step 1 : Write the given numbers in a horizontal line.
200 | 400 | 900 |
Step 2 : Divide the given numbers by smallest prime number. In this example we can divide by 2.
(if any number is not divisible by 2, write it down unchanged)
2 | 200 | 400 | 900 |
100 | 200 | 450 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
2 | 200 | 400 | 900 |
2 | 100 | 200 | 450 |
2 | 50 | 100 | 225 |
2 | 25 | 50 | 225 |
3 | 25 | 25 | 225 |
3 | 25 | 25 | 75 |
5 | 25 | 25 | 25 |
5 | 5 | 5 | 5 |
1 | 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 200, 400, 900 ) = 2 · 2 · 2 · 2 · 3 · 3 · 5 · 5 = 3600 .
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.