Question
Find Least Common Multiple of 16, 24, 15 and 35 using prime factorisation method.
Answer
LCM( 16, 24, 15, 35 ) = 1680
Explanation
Step 1: Write down factorisation of each number:
16 = 2 · 2 · 2 · 2
24 = 2 · 2 · 2 · 3
15 = 3 · 5
35 = 5 · 7
Step 2 : Match primes vertically:
| 16 | = | 2 | · | 2 | · | 2 | · | 2 | ||||||
| 24 | = | 2 | · | 2 | · | 2 | · | 3 | ||||||
| 15 | = | 3 | · | 5 | ||||||||||
| 35 | = | 5 | · | 7 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 16 | = | 2 | · | 2 | · | 2 | · | 2 | ||||||||
| 24 | = | 2 | · | 2 | · | 2 | · | 3 | ||||||||
| 15 | = | 3 | · | 5 | ||||||||||||
| 35 | = | 5 | · | 7 | ||||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 5 | · | 7 | = | 1680 |
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