Question
Find Least Common Multiple of 1741 and 2670467670 using division method..
Answer
LCM( 1741, 2670467670 ) = 2670467670
Explanation
Step 1 : Write the given numbers in a horizontal line.
| 1741 | 2670467670 |
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 | 1741 | 2670467670 |
| 1741 | 1335233835 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
| 2 | 1741 | 2670467670 |
| 3 | 1741 | 1335233835 |
| 3 | 1741 | 445077945 |
| 3 | 1741 | 148359315 |
| 5 | 1741 | 49453105 |
| 13 | 1741 | 9890621 |
| 19 | 1741 | 760817 |
| 23 | 1741 | 40043 |
| 1741 | 1741 | 1741 |
| 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 1741, 2670467670 ) = 2 · 3 · 3 · 3 · 5 · 13 · 19 · 23 · 1741 = 2670467670 .
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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