Question
Find Least Common Multiple of 1713 and 115833060 using division method..
Answer
LCM( 1713, 115833060 ) = 115833060
Explanation
Step 1 : Write the given numbers in a horizontal line.
| 1713 | 115833060 |
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 | 1713 | 115833060 |
| 1713 | 57916530 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
| 2 | 1713 | 115833060 |
| 2 | 1713 | 57916530 |
| 3 | 1713 | 28958265 |
| 3 | 571 | 9652755 |
| 5 | 571 | 3217585 |
| 7 | 571 | 643517 |
| 7 | 571 | 91931 |
| 23 | 571 | 13133 |
| 571 | 571 | 571 |
| 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 1713, 115833060 ) = 2 · 2 · 3 · 3 · 5 · 7 · 7 · 23 · 571 = 115833060 .
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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