Find Least Common Multiple of 24, 36, 120 and 18 using prime factorisation method.
Answer
LCM( 24, 36, 120, 18 ) = 360
Explanation
Step 1: Write down factorisation of each number:
24 = 2 · 2 · 2 · 3
36 = 2 · 2 · 3 · 3
120 = 2 · 2 · 2 · 3 · 5
18 = 2 · 3 · 3
Step 2 : Match primes vertically:
| 24 | = | 2 | · | 2 | · | 2 | · | 3 | ||||
| 36 | = | 2 | · | 2 | · | 3 | · | 3 | ||||
| 120 | = | 2 | · | 2 | · | 2 | · | 3 | · | 5 | ||
| 18 | = | 2 | · | 3 | · | 3 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 24 | = | 2 | · | 2 | · | 2 | · | 3 | ||||||
| 36 | = | 2 | · | 2 | · | 3 | · | 3 | ||||||
| 120 | = | 2 | · | 2 | · | 2 | · | 3 | · | 5 | ||||
| 18 | = | 2 | · | 3 | · | 3 | ||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 5 | = | 360 |
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