Question
Find Least Common Multiple of 36, 54, 108 and 144 using division method..
Answer
LCM( 36, 54, 108, 144 ) = 432
Explanation
Step 1 : Write the given numbers in a horizontal line.
| 36 | 54 | 108 | 144 |
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 | 36 | 54 | 108 | 144 |
| 18 | 27 | 54 | 72 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
| 2 | 36 | 54 | 108 | 144 |
| 2 | 18 | 27 | 54 | 72 |
| 2 | 9 | 27 | 27 | 36 |
| 2 | 9 | 27 | 27 | 18 |
| 3 | 9 | 27 | 27 | 9 |
| 3 | 3 | 9 | 9 | 3 |
| 3 | 1 | 3 | 3 | 1 |
| 1 | 1 | 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 36, 54, 108, 144 ) = 2 · 2 · 2 · 2 · 3 · 3 · 3 = 432 .
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