Question
Find Least Common Multiple of 56, 84 and 133 using prime factorisation method.
Answer
LCM( 56, 84, 133 ) = 3192
Explanation
Step 1: Write down factorisation of each number:
56 = 2 · 2 · 2 · 7
84 = 2 · 2 · 3 · 7
133 = 7 · 19
Step 2 : Match primes vertically:
| 56 | = | 2 | · | 2 | · | 2 | · | 7 | ||||
| 84 | = | 2 | · | 2 | · | 3 | · | 7 | ||||
| 133 | = | 7 | · | 19 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 56 | = | 2 | · | 2 | · | 2 | · | 7 | ||||||
| 84 | = | 2 | · | 2 | · | 3 | · | 7 | ||||||
| 133 | = | 7 | · | 19 | ||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 7 | · | 19 | = | 3192 |
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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