Question
Find Least Common Multiple of 70, 154 and 196 using division method..
Answer
LCM( 70, 154, 196 ) = 10780
Explanation
Step 1 : Write the given numbers in a horizontal line.
| 70 | 154 | 196 |
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 | 70 | 154 | 196 |
| 35 | 77 | 98 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
| 2 | 70 | 154 | 196 |
| 2 | 35 | 77 | 98 |
| 5 | 35 | 77 | 49 |
| 7 | 7 | 77 | 49 |
| 7 | 1 | 11 | 7 |
| 11 | 1 | 11 | 1 |
| 1 | 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 70, 154, 196 ) = 2 · 2 · 5 · 7 · 7 · 11 = 10780 .
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.
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