Question
Find Least Common Multiple of 45, 105 and 165 using division method..
Answer
LCM( 45, 105, 165 ) = 3465
Explanation
Step 1 : Write the given numbers in a horizontal line.
| 45 | 105 | 165 |
Step 2 : Divide the given numbers by smallest prime number. In this example we can divide by 3.
(if any number is not divisible by 3, write it down unchanged)
| 3 | 45 | 105 | 165 |
| 15 | 35 | 55 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
| 3 | 45 | 105 | 165 |
| 3 | 15 | 35 | 55 |
| 5 | 5 | 35 | 55 |
| 7 | 1 | 7 | 11 |
| 11 | 1 | 1 | 11 |
| 1 | 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 45, 105, 165 ) = 3 · 3 · 5 · 7 · 11 = 3465 .
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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