Question
Find Least Common Multiple of 81, 54, 30 and 27 using prime factorisation method.
Answer
LCM( 81, 54, 30, 27 ) = 810
Explanation
Step 1: Write down factorisation of each number:
81 = 3 · 3 · 3 · 3
54 = 2 · 3 · 3 · 3
30 = 2 · 3 · 5
27 = 3 · 3 · 3
Step 2 : Match primes vertically:
| 81 | = | 3 | · | 3 | · | 3 | · | 3 | ||||
| 54 | = | 2 | · | 3 | · | 3 | · | 3 | ||||
| 30 | = | 2 | · | 3 | · | 5 | ||||||
| 27 | = | 3 | · | 3 | · | 3 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 81 | = | 3 | · | 3 | · | 3 | · | 3 | ||||||
| 54 | = | 2 | · | 3 | · | 3 | · | 3 | ||||||
| 30 | = | 2 | · | 3 | · | 5 | ||||||||
| 27 | = | 3 | · | 3 | · | 3 | ||||||||
| LCM | = | 2 | · | 3 | · | 3 | · | 3 | · | 3 | · | 5 | = | 810 |
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