Find Least Common Multiple of 300, 456 and 120 using prime factorisation method.
Answer
LCM( 300, 456, 120 ) = 11400
Explanation
Step 1: Write down factorisation of each number:
300 = 2 · 2 · 3 · 5 · 5
456 = 2 · 2 · 2 · 3 · 19
120 = 2 · 2 · 2 · 3 · 5
Step 2 : Match primes vertically:
| 300 | = | 2 | · | 2 | · | 3 | · | 5 | · | 5 | ||||
| 456 | = | 2 | · | 2 | · | 2 | · | 3 | · | 19 | ||||
| 120 | = | 2 | · | 2 | · | 2 | · | 3 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 300 | = | 2 | · | 2 | · | 3 | · | 5 | · | 5 | ||||||
| 456 | = | 2 | · | 2 | · | 2 | · | 3 | · | 19 | ||||||
| 120 | = | 2 | · | 2 | · | 2 | · | 3 | · | 5 | ||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 5 | · | 5 | · | 19 | = | 11400 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.
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