Find Least Common Multiple of 2, 82, 26, 54 and 216 using prime factorisation method.
Answer
LCM( 2, 82, 26, 54, 216 ) = 115128
Explanation
Step 1: Write down factorisation of each number:
2 = 2
82 = 2 · 41
26 = 2 · 13
54 = 2 · 3 · 3 · 3
216 = 2 · 2 · 2 · 3 · 3 · 3
Step 2 : Match primes vertically:
| 2 | = | 2 | ||||||||||||||
| 82 | = | 2 | · | 41 | ||||||||||||
| 26 | = | 2 | · | 13 | ||||||||||||
| 54 | = | 2 | · | 3 | · | 3 | · | 3 | ||||||||
| 216 | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 3 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 2 | = | 2 | ||||||||||||||||
| 82 | = | 2 | · | 41 | ||||||||||||||
| 26 | = | 2 | · | 13 | ||||||||||||||
| 54 | = | 2 | · | 3 | · | 3 | · | 3 | ||||||||||
| 216 | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 3 | ||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 3 | · | 13 | · | 41 | = | 115128 |
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