Question
Find Least Common Multiple of 279 and 259 using division method..
Answer
LCM( 279, 259 ) = 72261
Explanation
Step 1 : Write the given numbers in a horizontal line.
| 279 | 259 |
Step 2 : Divide the given numbers by smallest prime number. In this example we can divide by 3.
(if any number is not divisible by 3, write it down unchanged)
| 3 | 279 | 259 |
| 93 | 259 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
| 3 | 279 | 259 |
| 3 | 93 | 259 |
| 7 | 31 | 259 |
| 31 | 31 | 37 |
| 37 | 1 | 37 |
| 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 279, 259 ) = 3 · 3 · 7 · 31 · 37 = 72261 .
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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