Question
Find Least Common Multiple of 1024 and 512 using division method..
Answer
LCM( 1024, 512 ) = 1024
Explanation
Step 1 : Write the given numbers in a horizontal line.
| 1024 | 512 |
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 | 1024 | 512 |
| 512 | 256 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
| 2 | 1024 | 512 |
| 2 | 512 | 256 |
| 2 | 256 | 128 |
| 2 | 128 | 64 |
| 2 | 64 | 32 |
| 2 | 32 | 16 |
| 2 | 16 | 8 |
| 2 | 8 | 4 |
| 2 | 4 | 2 |
| 2 | 2 | 1 |
| 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 1024, 512 ) = 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2 = 1024 .
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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