LCM( 108, 120, 132 ) = 11880
Step 1 : Write the given numbers in a horizontal line.
108 | 120 | 132 |
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 | 108 | 120 | 132 |
54 | 60 | 66 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
2 | 108 | 120 | 132 |
2 | 54 | 60 | 66 |
2 | 27 | 30 | 33 |
3 | 27 | 15 | 33 |
3 | 9 | 5 | 11 |
3 | 3 | 5 | 11 |
5 | 1 | 5 | 11 |
11 | 1 | 1 | 11 |
1 | 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 108, 120, 132 ) = 2 · 2 · 2 · 3 · 3 · 3 · 5 · 11 = 11880 .
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.