Find Least Common Multiple of 99, 55 and 76 using prime factorisation method.
Answer
LCM( 99, 55, 76 ) = 37620
Explanation
Step 1: Write down factorisation of each number:
99 = 3 · 3 · 11
55 = 5 · 11
76 = 2 · 2 · 19
Step 2 : Match primes vertically:
| 99 | = | 3 | · | 3 | · | 11 | ||||||||
| 55 | = | 5 | · | 11 | ||||||||||
| 76 | = | 2 | · | 2 | · | 19 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 99 | = | 3 | · | 3 | · | 11 | ||||||||||
| 55 | = | 5 | · | 11 | ||||||||||||
| 76 | = | 2 | · | 2 | · | 19 | ||||||||||
| LCM | = | 2 | · | 2 | · | 3 | · | 3 | · | 5 | · | 11 | · | 19 | = | 37620 |
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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