Question
Find Least Common Multiple of 429 and 406 using division method..
Answer
LCM( 429, 406 ) = 174174
Explanation
Step 1 : Write the given numbers in a horizontal line.
| 429 | 406 |
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 | 429 | 406 |
| 429 | 203 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
| 2 | 429 | 406 |
| 3 | 429 | 203 |
| 7 | 143 | 203 |
| 11 | 143 | 29 |
| 13 | 13 | 29 |
| 29 | 1 | 29 |
| 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 429, 406 ) = 2 · 3 · 7 · 11 · 13 · 29 = 174174 .
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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