Find Least Common Multiple of 72, 64 and 968 using prime factorisation method.
Answer
LCM( 72, 64, 968 ) = 69696
Explanation
Step 1: Write down factorisation of each number:
72 = 2 · 2 · 2 · 3 · 3
64 = 2 · 2 · 2 · 2 · 2 · 2
968 = 2 · 2 · 2 · 11 · 11
Step 2 : Match primes vertically:
| 72 | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | ||||||||||
| 64 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | ||||||||
| 968 | = | 2 | · | 2 | · | 2 | · | 11 | · | 11 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 72 | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | ||||||||||||
| 64 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | ||||||||||
| 968 | = | 2 | · | 2 | · | 2 | · | 11 | · | 11 | ||||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 11 | · | 11 | = | 69696 |
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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