Question
Find Least Common Multiple of 450 and 516 using division method..
Answer
LCM( 450, 516 ) = 38700
Explanation
Step 1 : Write the given numbers in a horizontal line.
| 450 | 516 |
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 | 450 | 516 |
| 225 | 258 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
| 2 | 450 | 516 |
| 2 | 225 | 258 |
| 3 | 225 | 129 |
| 3 | 75 | 43 |
| 5 | 25 | 43 |
| 5 | 5 | 43 |
| 43 | 1 | 43 |
| 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 450, 516 ) = 2 · 2 · 3 · 3 · 5 · 5 · 43 = 38700 .
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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