Find Least Common Multiple of 25, 24 and 32 using prime factorisation method.
Answer
LCM( 25, 24, 32 ) = 2400
Explanation
Step 1: Write down factorisation of each number:
25 = 5 · 5
24 = 2 · 2 · 2 · 3
32 = 2 · 2 · 2 · 2 · 2
Step 2 : Match primes vertically:
| 25 | = | 5 | · | 5 | ||||||||||||
| 24 | = | 2 | · | 2 | · | 2 | · | 3 | ||||||||
| 32 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 25 | = | 5 | · | 5 | ||||||||||||||
| 24 | = | 2 | · | 2 | · | 2 | · | 3 | ||||||||||
| 32 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | ||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 5 | · | 5 | = | 2400 |
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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