Question
Find Least Common Multiple of 22, 54, 108, 135 and 198 using division method..
Answer
LCM( 22, 54, 108, 135, 198 ) = 5940
Explanation
Step 1 : Write the given numbers in a horizontal line.
| 22 | 54 | 108 | 135 | 198 |
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 | 22 | 54 | 108 | 135 | 198 |
| 11 | 27 | 54 | 135 | 99 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
| 2 | 22 | 54 | 108 | 135 | 198 |
| 2 | 11 | 27 | 54 | 135 | 99 |
| 3 | 11 | 27 | 27 | 135 | 99 |
| 3 | 11 | 9 | 9 | 45 | 33 |
| 3 | 11 | 3 | 3 | 15 | 11 |
| 5 | 11 | 1 | 1 | 5 | 11 |
| 11 | 11 | 1 | 1 | 1 | 11 |
| 1 | 1 | 1 | 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 22, 54, 108, 135, 198 ) = 2 · 2 · 3 · 3 · 3 · 5 · 11 = 5940 .
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