Question
Find Least Common Multiple of 1740 and 386666280 using division method..
Answer
LCM( 1740, 386666280 ) = 386666280
Explanation
Step 1 : Write the given numbers in a horizontal line.
| 1740 | 386666280 |
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 | 1740 | 386666280 |
| 870 | 193333140 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
| 2 | 1740 | 386666280 |
| 2 | 870 | 193333140 |
| 2 | 435 | 96666570 |
| 3 | 435 | 48333285 |
| 3 | 145 | 16111095 |
| 5 | 145 | 5370365 |
| 7 | 29 | 1074073 |
| 11 | 29 | 153439 |
| 13 | 29 | 13949 |
| 29 | 29 | 1073 |
| 37 | 1 | 37 |
| 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 1740, 386666280 ) = 2 · 2 · 2 · 3 · 3 · 5 · 7 · 11 · 13 · 29 · 37 = 386666280 .
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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