LCM( 48, 80, 112 ) = 1680
Step 1 : Write the given numbers in a horizontal line.
48 | 80 | 112 |
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 | 80 | 112 |
24 | 40 | 56 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
2 | 48 | 80 | 112 |
2 | 24 | 40 | 56 |
2 | 12 | 20 | 28 |
2 | 6 | 10 | 14 |
3 | 3 | 5 | 7 |
5 | 1 | 5 | 7 |
7 | 1 | 1 | 7 |
1 | 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 48, 80, 112 ) = 2 · 2 · 2 · 2 · 3 · 5 · 7 = 1680 .
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.