Find Least Common Multiple of 15, 90, 12 and 8 using prime factorisation method.
Answer
LCM( 15, 90, 12, 8 ) = 360
Explanation
Step 1: Write down factorisation of each number:
15 = 3 · 5
90 = 2 · 3 · 3 · 5
12 = 2 · 2 · 3
8 = 2 · 2 · 2
Step 2 : Match primes vertically:
| 15 | = | 3 | · | 5 | ||||||||
| 90 | = | 2 | · | 3 | · | 3 | · | 5 | ||||
| 12 | = | 2 | · | 2 | · | 3 | ||||||
| 8 | = | 2 | · | 2 | · | 2 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 15 | = | 3 | · | 5 | ||||||||||
| 90 | = | 2 | · | 3 | · | 3 | · | 5 | ||||||
| 12 | = | 2 | · | 2 | · | 3 | ||||||||
| 8 | = | 2 | · | 2 | · | 2 | ||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 5 | = | 360 |
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