Find Least Common Multiple of 12, 24, 42 and 60 using prime factorisation method.
Answer
LCM( 12, 24, 42, 60 ) = 840
Explanation
Step 1: Write down factorisation of each number:
12 = 2 · 2 · 3
24 = 2 · 2 · 2 · 3
42 = 2 · 3 · 7
60 = 2 · 2 · 3 · 5
Step 2 : Match primes vertically:
| 12 | = | 2 | · | 2 | · | 3 | ||||||
| 24 | = | 2 | · | 2 | · | 2 | · | 3 | ||||
| 42 | = | 2 | · | 3 | · | 7 | ||||||
| 60 | = | 2 | · | 2 | · | 3 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 12 | = | 2 | · | 2 | · | 3 | ||||||||
| 24 | = | 2 | · | 2 | · | 2 | · | 3 | ||||||
| 42 | = | 2 | · | 3 | · | 7 | ||||||||
| 60 | = | 2 | · | 2 | · | 3 | · | 5 | ||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 5 | · | 7 | = | 840 |
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