Find Least Common Multiple of 180, 200 and 420 using division method..
Answer
LCM( 180, 200, 420 ) = 12600
Explanation
Step 1 : Write the given numbers in a horizontal line.
| 180 | 200 | 420 |
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 | 180 | 200 | 420 |
| 90 | 100 | 210 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
| 2 | 180 | 200 | 420 |
| 2 | 90 | 100 | 210 |
| 2 | 45 | 50 | 105 |
| 3 | 45 | 25 | 105 |
| 3 | 15 | 25 | 35 |
| 5 | 5 | 25 | 35 |
| 5 | 1 | 5 | 7 |
| 7 | 1 | 1 | 7 |
| 1 | 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 180, 200, 420 ) = 2 · 2 · 2 · 3 · 3 · 5 · 5 · 7 = 12600 .
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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