Question
Find Least Common Multiple of 10 and 1000 using prime factorisation method.
Answer
LCM( 10, 1000 ) = 1000
Explanation
Step 1: Write down factorisation of each number:
10 = 2 · 5
1000 = 2 · 2 · 2 · 5 · 5 · 5
Step 2 : Match primes vertically:
| 10 | = | 2 | · | 5 | ||||||||
| 1000 | = | 2 | · | 2 | · | 2 | · | 5 | · | 5 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 10 | = | 2 | · | 5 | ||||||||||
| 1000 | = | 2 | · | 2 | · | 2 | · | 5 | · | 5 | · | 5 | ||
| LCM | = | 2 | · | 2 | · | 2 | · | 5 | · | 5 | · | 5 | = | 1000 |
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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