Find Least Common Multiple of 288, 300 and 224 using prime factorisation method.
Answer
LCM( 288, 300, 224 ) = 50400
Explanation
Step 1: Write down factorisation of each number:
288 = 2 · 2 · 2 · 2 · 2 · 3 · 3
300 = 2 · 2 · 3 · 5 · 5
224 = 2 · 2 · 2 · 2 · 2 · 7
Step 2 : Match primes vertically:
| 288 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | ||||||
| 300 | = | 2 | · | 2 | · | 3 | · | 5 | · | 5 | ||||||||||
| 224 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 7 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 288 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | ||||||||
| 300 | = | 2 | · | 2 | · | 3 | · | 5 | · | 5 | ||||||||||||
| 224 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 7 | ||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 5 | · | 5 | · | 7 | = | 50400 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.
This page was created using
LCM Calculator