Find Least Common Multiple of 16, 12, 18, 20 and 16 using prime factorisation method.
Answer
LCM( 16, 12, 18, 20, 16 ) = 720
Explanation
Step 1: Write down factorisation of each number:
16 = 2 · 2 · 2 · 2
12 = 2 · 2 · 3
18 = 2 · 3 · 3
20 = 2 · 2 · 5
16 = 2 · 2 · 2 · 2
Step 2 : Match primes vertically:
| 16 | = | 2 | · | 2 | · | 2 | · | 2 | ||||||
| 12 | = | 2 | · | 2 | · | 3 | ||||||||
| 18 | = | 2 | · | 3 | · | 3 | ||||||||
| 20 | = | 2 | · | 2 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 16 | = | 2 | · | 2 | · | 2 | · | 2 | ||||||||
| 12 | = | 2 | · | 2 | · | 3 | ||||||||||
| 18 | = | 2 | · | 3 | · | 3 | ||||||||||
| 20 | = | 2 | · | 2 | · | 5 | ||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 5 | = | 720 |
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