Question
Find Least Common Multiple of 1400, 1800 and 1920 using prime factorisation method.
Answer
LCM( 1400, 1800, 1920 ) = 201600
Explanation
Step 1: Write down factorisation of each number:
1400 = 2 · 2 · 2 · 5 · 5 · 7
1800 = 2 · 2 · 2 · 3 · 3 · 5 · 5
1920 = 2 · 2 · 2 · 2 · 2 · 2 · 2 · 3 · 5
Step 2 : Match primes vertically:
| 1400 | = | 2 | · | 2 | · | 2 | · | 5 | · | 5 | · | 7 | ||||||||||||
| 1800 | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 5 | · | 5 | ||||||||||
| 1920 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 1400 | = | 2 | · | 2 | · | 2 | · | 5 | · | 5 | · | 7 | ||||||||||||||
| 1800 | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 5 | · | 5 | ||||||||||||
| 1920 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 5 | ||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 5 | · | 5 | · | 7 | = | 201600 |
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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