Question
Find Least Common Multiple of 143, 60, 120 and 225 using prime factorisation method.
Answer
LCM( 143, 60, 120, 225 ) = 257400
Explanation
Step 1: Write down factorisation of each number:
143 = 11 · 13
60 = 2 · 2 · 3 · 5
120 = 2 · 2 · 2 · 3 · 5
225 = 3 · 3 · 5 · 5
Step 2 : Match primes vertically:
| 143 | = | 11 | · | 13 | ||||||||||||||
| 60 | = | 2 | · | 2 | · | 3 | · | 5 | ||||||||||
| 120 | = | 2 | · | 2 | · | 2 | · | 3 | · | 5 | ||||||||
| 225 | = | 3 | · | 3 | · | 5 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 143 | = | 11 | · | 13 | ||||||||||||||||
| 60 | = | 2 | · | 2 | · | 3 | · | 5 | ||||||||||||
| 120 | = | 2 | · | 2 | · | 2 | · | 3 | · | 5 | ||||||||||
| 225 | = | 3 | · | 3 | · | 5 | · | 5 | ||||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 5 | · | 5 | · | 11 | · | 13 | = | 257400 |
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