Question
Find Least Common Multiple of 1700 and 21348600 using division method..
Answer
LCM( 1700, 21348600 ) = 21348600
Explanation
Step 1 : Write the given numbers in a horizontal line.
| 1700 | 21348600 |
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 | 1700 | 21348600 |
| 850 | 10674300 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
| 2 | 1700 | 21348600 |
| 2 | 850 | 10674300 |
| 2 | 425 | 5337150 |
| 3 | 425 | 2668575 |
| 5 | 425 | 889525 |
| 5 | 85 | 177905 |
| 7 | 17 | 35581 |
| 13 | 17 | 5083 |
| 17 | 17 | 391 |
| 23 | 1 | 23 |
| 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 1700, 21348600 ) = 2 · 2 · 2 · 3 · 5 · 5 · 7 · 13 · 17 · 23 = 21348600 .
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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