Find Least Common Multiple of 12, 24, 72 and 75 using prime factorisation method.
Answer
LCM( 12, 24, 72, 75 ) = 1800
Explanation
Step 1: Write down factorisation of each number:
12 = 2 · 2 · 3
24 = 2 · 2 · 2 · 3
72 = 2 · 2 · 2 · 3 · 3
75 = 3 · 5 · 5
Step 2 : Match primes vertically:
| 12 | = | 2 | · | 2 | · | 3 | ||||||||
| 24 | = | 2 | · | 2 | · | 2 | · | 3 | ||||||
| 72 | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | ||||
| 75 | = | 3 | · | 5 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 12 | = | 2 | · | 2 | · | 3 | ||||||||||
| 24 | = | 2 | · | 2 | · | 2 | · | 3 | ||||||||
| 72 | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | ||||||
| 75 | = | 3 | · | 5 | · | 5 | ||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 5 | · | 5 | = | 1800 |
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