LCM( 140, 56, 210 ) = 840
Step 1 : Write the given numbers in a horizontal line.
140 | 56 | 210 |
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 | 140 | 56 | 210 |
70 | 28 | 105 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
2 | 140 | 56 | 210 |
2 | 70 | 28 | 105 |
2 | 35 | 14 | 105 |
3 | 35 | 7 | 105 |
5 | 35 | 7 | 35 |
7 | 7 | 7 | 7 |
1 | 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 140, 56, 210 ) = 2 · 2 · 2 · 3 · 5 · 7 = 840 .
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.