Find Least Common Multiple of 45, 54 and 81 using division method..
Answer
LCM( 45, 54, 81 ) = 810
Explanation
Step 1 : Write the given numbers in a horizontal line.
| 45 | 54 | 81 |
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 | 45 | 54 | 81 |
| 45 | 27 | 81 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
| 2 | 45 | 54 | 81 |
| 3 | 45 | 27 | 81 |
| 3 | 15 | 9 | 27 |
| 3 | 5 | 3 | 9 |
| 3 | 5 | 1 | 3 |
| 5 | 5 | 1 | 1 |
| 1 | 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 45, 54, 81 ) = 2 · 3 · 3 · 3 · 3 · 5 = 810 .
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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