Question
Find Least Common Multiple of 1729 and 311220 using division method..
Answer
LCM( 1729, 311220 ) = 311220
Explanation
Step 1 : Write the given numbers in a horizontal line.
| 1729 | 311220 |
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 | 1729 | 311220 |
| 1729 | 155610 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
| 2 | 1729 | 311220 |
| 2 | 1729 | 155610 |
| 3 | 1729 | 77805 |
| 3 | 1729 | 25935 |
| 5 | 1729 | 8645 |
| 7 | 1729 | 1729 |
| 13 | 247 | 247 |
| 19 | 19 | 19 |
| 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 1729, 311220 ) = 2 · 2 · 3 · 3 · 5 · 7 · 13 · 19 = 311220 .
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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