Find Least Common Multiple of 312, 18 and 39 using prime factorisation method.
Answer
LCM( 312, 18, 39 ) = 936
Explanation
Step 1: Write down factorisation of each number:
312 = 2 · 2 · 2 · 3 · 13
18 = 2 · 3 · 3
39 = 3 · 13
Step 2 : Match primes vertically:
| 312 | = | 2 | · | 2 | · | 2 | · | 3 | · | 13 | ||
| 18 | = | 2 | · | 3 | · | 3 | ||||||
| 39 | = | 3 | · | 13 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 312 | = | 2 | · | 2 | · | 2 | · | 3 | · | 13 | ||||
| 18 | = | 2 | · | 3 | · | 3 | ||||||||
| 39 | = | 3 | · | 13 | ||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 13 | = | 936 |
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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