Question
Find Least Common Multiple of 17, 24 and 53 using prime factorisation method.
Answer
LCM( 17, 24, 53 ) = 21624
Explanation
Step 1: Write down factorisation of each number:
17 = 17
24 = 2 · 2 · 2 · 3
53 = 53
Step 2 : Match primes vertically:
| 17 | = | 17 | ||||||||||
| 24 | = | 2 | · | 2 | · | 2 | · | 3 | ||||
| 53 | = | 53 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 17 | = | 17 | ||||||||||||
| 24 | = | 2 | · | 2 | · | 2 | · | 3 | ||||||
| 53 | = | 53 | ||||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 17 | · | 53 | = | 21624 |
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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