Find Least Common Multiple of 31, 82 and 77 using division method..
Answer
LCM( 31, 82, 77 ) = 195734
Explanation
Step 1 : Write the given numbers in a horizontal line.
| 31 | 82 | 77 |
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 | 31 | 82 | 77 |
| 31 | 41 | 77 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
| 2 | 31 | 82 | 77 |
| 7 | 31 | 41 | 77 |
| 11 | 31 | 41 | 11 |
| 31 | 31 | 41 | 1 |
| 41 | 1 | 41 | 1 |
| 1 | 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 31, 82, 77 ) = 2 · 7 · 11 · 31 · 41 = 195734 .
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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