Question
Find Least Common Multiple of 1240, 1750 and 2300 using division method..
Answer
LCM( 1240, 1750, 2300 ) = 4991000
Explanation
Step 1 : Write the given numbers in a horizontal line.
| 1240 | 1750 | 2300 |
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 | 1240 | 1750 | 2300 |
| 620 | 875 | 1150 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
| 2 | 1240 | 1750 | 2300 |
| 2 | 620 | 875 | 1150 |
| 2 | 310 | 875 | 575 |
| 5 | 155 | 875 | 575 |
| 5 | 31 | 175 | 115 |
| 5 | 31 | 35 | 23 |
| 7 | 31 | 7 | 23 |
| 23 | 31 | 1 | 23 |
| 31 | 31 | 1 | 1 |
| 1 | 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 1240, 1750, 2300 ) = 2 · 2 · 2 · 5 · 5 · 5 · 7 · 23 · 31 = 4991000 .
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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