Question
Find Least Common Multiple of 444, 892 and 66 using division method..
Answer
LCM( 444, 892, 66 ) = 1089132
Explanation
Step 1 : Write the given numbers in a horizontal line.
| 444 | 892 | 66 |
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 | 444 | 892 | 66 |
| 222 | 446 | 33 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
| 2 | 444 | 892 | 66 |
| 2 | 222 | 446 | 33 |
| 3 | 111 | 223 | 33 |
| 11 | 37 | 223 | 11 |
| 37 | 37 | 223 | 1 |
| 223 | 1 | 223 | 1 |
| 1 | 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 444, 892, 66 ) = 2 · 2 · 3 · 11 · 37 · 223 = 1089132 .
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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