Question
Find Least Common Multiple of 1750 and 174174000 using division method..
Answer
LCM( 1750, 174174000 ) = 174174000
Explanation
Step 1 : Write the given numbers in a horizontal line.
| 1750 | 174174000 |
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 | 1750 | 174174000 |
| 875 | 87087000 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
| 2 | 1750 | 174174000 |
| 2 | 875 | 87087000 |
| 2 | 875 | 43543500 |
| 2 | 875 | 21771750 |
| 3 | 875 | 10885875 |
| 5 | 875 | 3628625 |
| 5 | 175 | 725725 |
| 5 | 35 | 145145 |
| 7 | 7 | 29029 |
| 11 | 1 | 4147 |
| 13 | 1 | 377 |
| 29 | 1 | 29 |
| 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 1750, 174174000 ) = 2 · 2 · 2 · 2 · 3 · 5 · 5 · 5 · 7 · 11 · 13 · 29 = 174174000 .
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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