LCM( 84, 126, 288 ) = 2016
Step 1 : Write the given numbers in a horizontal line.
84 | 126 | 288 |
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 | 84 | 126 | 288 |
42 | 63 | 144 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
2 | 84 | 126 | 288 |
2 | 42 | 63 | 144 |
2 | 21 | 63 | 72 |
2 | 21 | 63 | 36 |
2 | 21 | 63 | 18 |
3 | 21 | 63 | 9 |
3 | 7 | 21 | 3 |
7 | 7 | 7 | 1 |
1 | 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 84, 126, 288 ) = 2 · 2 · 2 · 2 · 2 · 3 · 3 · 7 = 2016 .
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.