Find Least Common Multiple of 16, 32, 18 and 36 using prime factorisation method.
Answer
LCM( 16, 32, 18, 36 ) = 288
Explanation
Step 1: Write down factorisation of each number:
16 = 2 · 2 · 2 · 2
32 = 2 · 2 · 2 · 2 · 2
18 = 2 · 3 · 3
36 = 2 · 2 · 3 · 3
Step 2 : Match primes vertically:
| 16 | = | 2 | · | 2 | · | 2 | · | 2 | ||||||
| 32 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | ||||
| 18 | = | 2 | · | 3 | · | 3 | ||||||||
| 36 | = | 2 | · | 2 | · | 3 | · | 3 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 16 | = | 2 | · | 2 | · | 2 | · | 2 | ||||||||
| 32 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | ||||||
| 18 | = | 2 | · | 3 | · | 3 | ||||||||||
| 36 | = | 2 | · | 2 | · | 3 | · | 3 | ||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | = | 288 |
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