Question
Find Least Common Multiple of 369 and 345 using division method..
Answer
LCM( 369, 345 ) = 42435
Explanation
Step 1 : Write the given numbers in a horizontal line.
| 369 | 345 |
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 | 369 | 345 |
| 123 | 115 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
| 3 | 369 | 345 |
| 3 | 123 | 115 |
| 5 | 41 | 115 |
| 23 | 41 | 23 |
| 41 | 41 | 1 |
| 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 369, 345 ) = 3 · 3 · 5 · 23 · 41 = 42435 .
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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