Question
Find Least Common Multiple of 1719 and 1439146800 using division method..
Answer
LCM( 1719, 1439146800 ) = 1439146800
Explanation
Step 1 : Write the given numbers in a horizontal line.
| 1719 | 1439146800 |
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 | 1719 | 1439146800 |
| 1719 | 719573400 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
| 2 | 1719 | 1439146800 |
| 2 | 1719 | 719573400 |
| 2 | 1719 | 359786700 |
| 2 | 1719 | 179893350 |
| 3 | 1719 | 89946675 |
| 3 | 573 | 29982225 |
| 5 | 191 | 9994075 |
| 5 | 191 | 1998815 |
| 7 | 191 | 399763 |
| 13 | 191 | 57109 |
| 23 | 191 | 4393 |
| 191 | 191 | 191 |
| 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 1719, 1439146800 ) = 2 · 2 · 2 · 2 · 3 · 3 · 5 · 5 · 7 · 13 · 23 · 191 = 1439146800 .
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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