Find Least Common Multiple of 16, 30 and 42 using prime factorisation method.
Answer
LCM( 16, 30, 42 ) = 1680
Explanation
Step 1: Write down factorisation of each number:
16 = 2 · 2 · 2 · 2
30 = 2 · 3 · 5
42 = 2 · 3 · 7
Step 2 : Match primes vertically:
| 16 | = | 2 | · | 2 | · | 2 | · | 2 | ||||||
| 30 | = | 2 | · | 3 | · | 5 | ||||||||
| 42 | = | 2 | · | 3 | · | 7 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 16 | = | 2 | · | 2 | · | 2 | · | 2 | ||||||||
| 30 | = | 2 | · | 3 | · | 5 | ||||||||||
| 42 | = | 2 | · | 3 | · | 7 | ||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 5 | · | 7 | = | 1680 |
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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