Question
Find Least Common Multiple of 40, 21, 18 and 12 using prime factorisation method.
Answer
LCM( 40, 21, 18, 12 ) = 2520
Explanation
Step 1: Write down factorisation of each number:
40 = 2 · 2 · 2 · 5
21 = 3 · 7
18 = 2 · 3 · 3
12 = 2 · 2 · 3
Step 2 : Match primes vertically:
| 40 | = | 2 | · | 2 | · | 2 | · | 5 | ||||||
| 21 | = | 3 | · | 7 | ||||||||||
| 18 | = | 2 | · | 3 | · | 3 | ||||||||
| 12 | = | 2 | · | 2 | · | 3 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 40 | = | 2 | · | 2 | · | 2 | · | 5 | ||||||||
| 21 | = | 3 | · | 7 | ||||||||||||
| 18 | = | 2 | · | 3 | · | 3 | ||||||||||
| 12 | = | 2 | · | 2 | · | 3 | ||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 5 | · | 7 | = | 2520 |
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