Question
Find Least Common Multiple of 1120, 64 and 1280 using prime factorisation method.
Answer
LCM( 1120, 64, 1280 ) = 8960
Explanation
Step 1: Write down factorisation of each number:
1120 = 2 · 2 · 2 · 2 · 2 · 5 · 7
64 = 2 · 2 · 2 · 2 · 2 · 2
1280 = 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2 · 5
Step 2 : Match primes vertically:
| 1120 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 5 | · | 7 | ||||||
| 64 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | ||||||||
| 1280 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 1120 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 5 | · | 7 | ||||||||
| 64 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | ||||||||||
| 1280 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 5 | ||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 5 | · | 7 | = | 8960 |
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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