Answer: 12
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Step-by-step explanation:
The given fractions are 2/3, 5/6, and 9/4.
The denominators are 3, 6, and 4 in that order.
Let's find the prime factorization of each denominator.
The unique primes are 2 and 3. The value 1 is not prime.
- "2" shows up at most twice, so 2^2 = 4 is one factor of the LCM.
- "3" shows up at most once, so 3^1 = 3 is the other factor of the LCM.
The LCM is therefore 4*3 = 12
The LCD is 12 since the LCD is the LCM of the denominators.
We can rewrite each fraction in terms of the LCD.
- 2/3 = (2/3)*(4/4) = 8/12
- 5/6 = (5/6)*(2/2) = 10/12
- 9/4 = (9/4)*(3/3) = 27/12
The reason why we care about the LCD is because it helps us add or subtract fractions. Recall that the denominators must be the same for this to happen.
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Another approach to find the LCM is to list the multiples of each. I'll mark in bold where the LCM shows up for each denominator.
- multiples of 3 are: 3, 6, 9, 12, 15, 18, ...
- multiples of 6 are: 6, 12, 18, 24, ...
- multiples of 4 are: 4, 8, 12, 16, 20, ...
We see that 12 is the smallest multiple in each list. Therefore, it is the LCM.