Question
Find Least Common Multiple of 180, 384 and 500 using division method..
Answer
LCM( 180, 384, 500 ) = 144000
Explanation
Step 1 : Write the given numbers in a horizontal line.
| 180 | 384 | 500 |
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 | 384 | 500 |
| 90 | 192 | 250 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
| 2 | 180 | 384 | 500 |
| 2 | 90 | 192 | 250 |
| 2 | 45 | 96 | 125 |
| 2 | 45 | 48 | 125 |
| 2 | 45 | 24 | 125 |
| 2 | 45 | 12 | 125 |
| 2 | 45 | 6 | 125 |
| 3 | 45 | 3 | 125 |
| 3 | 15 | 1 | 125 |
| 5 | 5 | 1 | 125 |
| 5 | 1 | 1 | 25 |
| 5 | 1 | 1 | 5 |
| 1 | 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 180, 384, 500 ) = 2 · 2 · 2 · 2 · 2 · 2 · 2 · 3 · 3 · 5 · 5 · 5 = 144000 .
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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