Question
Find Least Common Multiple of 1759 and 1682202060 using division method..
Answer
LCM( 1759, 1682202060 ) = 1682202060
Explanation
Step 1 : Write the given numbers in a horizontal line.
| 1759 | 1682202060 |
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 | 1759 | 1682202060 |
| 1759 | 841101030 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
| 2 | 1759 | 1682202060 |
| 2 | 1759 | 841101030 |
| 3 | 1759 | 420550515 |
| 3 | 1759 | 140183505 |
| 3 | 1759 | 46727835 |
| 5 | 1759 | 15575945 |
| 7 | 1759 | 3115189 |
| 11 | 1759 | 445027 |
| 23 | 1759 | 40457 |
| 1759 | 1759 | 1759 |
| 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 1759, 1682202060 ) = 2 · 2 · 3 · 3 · 3 · 5 · 7 · 11 · 23 · 1759 = 1682202060 .
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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