Question
Find Least Common Multiple of 696, 376 and 756 using division method..
Answer
LCM( 696, 376, 756 ) = 2060856
Explanation
Step 1 : Write the given numbers in a horizontal line.
| 696 | 376 | 756 |
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 | 696 | 376 | 756 |
| 348 | 188 | 378 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
| 2 | 696 | 376 | 756 |
| 2 | 348 | 188 | 378 |
| 2 | 174 | 94 | 189 |
| 3 | 87 | 47 | 189 |
| 3 | 29 | 47 | 63 |
| 3 | 29 | 47 | 21 |
| 7 | 29 | 47 | 7 |
| 29 | 29 | 47 | 1 |
| 47 | 1 | 47 | 1 |
| 1 | 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 696, 376, 756 ) = 2 · 2 · 2 · 3 · 3 · 3 · 7 · 29 · 47 = 2060856 .
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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