Find Least Common Multiple of 20, 36, 105 and 102 using prime factorisation method.
Answer
LCM( 20, 36, 105, 102 ) = 21420
Explanation
Step 1: Write down factorisation of each number:
20 = 2 · 2 · 5
36 = 2 · 2 · 3 · 3
105 = 3 · 5 · 7
102 = 2 · 3 · 17
Step 2 : Match primes vertically:
| 20 | = | 2 | · | 2 | · | 5 | ||||||||
| 36 | = | 2 | · | 2 | · | 3 | · | 3 | ||||||
| 105 | = | 3 | · | 5 | · | 7 | ||||||||
| 102 | = | 2 | · | 3 | · | 17 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 20 | = | 2 | · | 2 | · | 5 | ||||||||||
| 36 | = | 2 | · | 2 | · | 3 | · | 3 | ||||||||
| 105 | = | 3 | · | 5 | · | 7 | ||||||||||
| 102 | = | 2 | · | 3 | · | 17 | ||||||||||
| LCM | = | 2 | · | 2 | · | 3 | · | 3 | · | 5 | · | 7 | · | 17 | = | 21420 |
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