Question
Find Least Common Multiple of 1730 and 7823060 using division method..
Answer
LCM( 1730, 7823060 ) = 7823060
Explanation
Step 1 : Write the given numbers in a horizontal line.
| 1730 | 7823060 |
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 | 1730 | 7823060 |
| 865 | 3911530 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
| 2 | 1730 | 7823060 |
| 2 | 865 | 3911530 |
| 5 | 865 | 1955765 |
| 7 | 173 | 391153 |
| 17 | 173 | 55879 |
| 19 | 173 | 3287 |
| 173 | 173 | 173 |
| 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 1730, 7823060 ) = 2 · 2 · 5 · 7 · 17 · 19 · 173 = 7823060 .
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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