Find Least Common Multiple of 21, 28, 36 and 45 using prime factorisation method.
Answer
LCM( 21, 28, 36, 45 ) = 1260
Explanation
Step 1: Write down factorisation of each number:
21 = 3 · 7
28 = 2 · 2 · 7
36 = 2 · 2 · 3 · 3
45 = 3 · 3 · 5
Step 2 : Match primes vertically:
| 21 | = | 3 | · | 7 | ||||||||
| 28 | = | 2 | · | 2 | · | 7 | ||||||
| 36 | = | 2 | · | 2 | · | 3 | · | 3 | ||||
| 45 | = | 3 | · | 3 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 21 | = | 3 | · | 7 | ||||||||||
| 28 | = | 2 | · | 2 | · | 7 | ||||||||
| 36 | = | 2 | · | 2 | · | 3 | · | 3 | ||||||
| 45 | = | 3 | · | 3 | · | 5 | ||||||||
| LCM | = | 2 | · | 2 | · | 3 | · | 3 | · | 5 | · | 7 | = | 1260 |
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