LCM( 48, 108, 140 ) = 15120
Step 1 : Write the given numbers in a horizontal line.
48 | 108 | 140 |
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 | 48 | 108 | 140 |
24 | 54 | 70 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
2 | 48 | 108 | 140 |
2 | 24 | 54 | 70 |
2 | 12 | 27 | 35 |
2 | 6 | 27 | 35 |
3 | 3 | 27 | 35 |
3 | 1 | 9 | 35 |
3 | 1 | 3 | 35 |
5 | 1 | 1 | 35 |
7 | 1 | 1 | 7 |
1 | 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 48, 108, 140 ) = 2 · 2 · 2 · 2 · 3 · 3 · 3 · 5 · 7 = 15120 .
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.