Find Least Common Multiple of 564 and 300 using prime factorisation method.
Answer
LCM( 564, 300 ) = 14100
Explanation
Step 1: Write down factorisation of each number:
564 = 2 · 2 · 3 · 47
300 = 2 · 2 · 3 · 5 · 5
Step 2 : Match primes vertically:
| 564 | = | 2 | · | 2 | · | 3 | · | 47 | ||||
| 300 | = | 2 | · | 2 | · | 3 | · | 5 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 564 | = | 2 | · | 2 | · | 3 | · | 47 | ||||||
| 300 | = | 2 | · | 2 | · | 3 | · | 5 | · | 5 | ||||
| LCM | = | 2 | · | 2 | · | 3 | · | 5 | · | 5 | · | 47 | = | 14100 |
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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