Question
Find Least Common Multiple of 1737 and 45839430 using division method..
Answer
LCM( 1737, 45839430 ) = 45839430
Explanation
Step 1 : Write the given numbers in a horizontal line.
| 1737 | 45839430 |
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 | 1737 | 45839430 |
| 1737 | 22919715 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
| 2 | 1737 | 45839430 |
| 3 | 1737 | 22919715 |
| 3 | 579 | 7639905 |
| 5 | 193 | 2546635 |
| 7 | 193 | 509327 |
| 13 | 193 | 72761 |
| 29 | 193 | 5597 |
| 193 | 193 | 193 |
| 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 1737, 45839430 ) = 2 · 3 · 3 · 5 · 7 · 13 · 29 · 193 = 45839430 .
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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