Question
Find Least Common Multiple of 400, 620 and 780 using division method..
Answer
LCM( 400, 620, 780 ) = 483600
Explanation
Step 1 : Write the given numbers in a horizontal line.
| 400 | 620 | 780 |
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 | 400 | 620 | 780 |
| 200 | 310 | 390 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
| 2 | 400 | 620 | 780 |
| 2 | 200 | 310 | 390 |
| 2 | 100 | 155 | 195 |
| 2 | 50 | 155 | 195 |
| 3 | 25 | 155 | 195 |
| 5 | 25 | 155 | 65 |
| 5 | 5 | 31 | 13 |
| 13 | 1 | 31 | 13 |
| 31 | 1 | 31 | 1 |
| 1 | 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 400, 620, 780 ) = 2 · 2 · 2 · 2 · 3 · 5 · 5 · 13 · 31 = 483600 .
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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