Find Least Common Multiple of 121, 84 and 64 using prime factorisation method.
Answer
LCM( 121, 84, 64 ) = 162624
Explanation
Step 1: Write down factorisation of each number:
121 = 11 · 11
84 = 2 · 2 · 3 · 7
64 = 2 · 2 · 2 · 2 · 2 · 2
Step 2 : Match primes vertically:
| 121 | = | 11 | · | 11 | ||||||||||||||||
| 84 | = | 2 | · | 2 | · | 3 | · | 7 | ||||||||||||
| 64 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 121 | = | 11 | · | 11 | ||||||||||||||||||
| 84 | = | 2 | · | 2 | · | 3 | · | 7 | ||||||||||||||
| 64 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | ||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 7 | · | 11 | · | 11 | = | 162624 |
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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