Find Least Common Multiple of 820, 520 and 480 using prime factorisation method.
Answer
LCM( 820, 520, 480 ) = 255840
Explanation
Step 1: Write down factorisation of each number:
820 = 2 · 2 · 5 · 41
520 = 2 · 2 · 2 · 5 · 13
480 = 2 · 2 · 2 · 2 · 2 · 3 · 5
Step 2 : Match primes vertically:
| 820 | = | 2 | · | 2 | · | 5 | · | 41 | ||||||||||
| 520 | = | 2 | · | 2 | · | 2 | · | 5 | · | 13 | ||||||||
| 480 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 820 | = | 2 | · | 2 | · | 5 | · | 41 | ||||||||||||
| 520 | = | 2 | · | 2 | · | 2 | · | 5 | · | 13 | ||||||||||
| 480 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 5 | ||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 5 | · | 13 | · | 41 | = | 255840 |
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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