Question
Find Least Common Multiple of 19, 14 and 8 using prime factorisation method.
Answer
LCM( 19, 14, 8 ) = 1064
Explanation
Step 1: Write down factorisation of each number:
19 = 19
14 = 2 · 7
8 = 2 · 2 · 2
Step 2 : Match primes vertically:
| 19 | = | 19 | ||||||||
| 14 | = | 2 | · | 7 | ||||||
| 8 | = | 2 | · | 2 | · | 2 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 19 | = | 19 | ||||||||||
| 14 | = | 2 | · | 7 | ||||||||
| 8 | = | 2 | · | 2 | · | 2 | ||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 7 | · | 19 | = | 1064 |
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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