Question
Find Least Common Multiple of 100, 220 and 470 using prime factorisation method.
Answer
LCM( 100, 220, 470 ) = 51700
Explanation
Step 1: Write down factorisation of each number:
100 = 2 · 2 · 5 · 5
220 = 2 · 2 · 5 · 11
470 = 2 · 5 · 47
Step 2 : Match primes vertically:
| 100 | = | 2 | · | 2 | · | 5 | · | 5 | ||||
| 220 | = | 2 | · | 2 | · | 5 | · | 11 | ||||
| 470 | = | 2 | · | 5 | · | 47 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 100 | = | 2 | · | 2 | · | 5 | · | 5 | ||||||
| 220 | = | 2 | · | 2 | · | 5 | · | 11 | ||||||
| 470 | = | 2 | · | 5 | · | 47 | ||||||||
| LCM | = | 2 | · | 2 | · | 5 | · | 5 | · | 11 | · | 47 | = | 51700 |
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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