Question

Which of the following whole numbers could not be used as a common denominator to add the tions:

a) 64
b) 72
c) 96
d) 48

Answer 1

To determine a common denominator for adding fractions, we find the least common multiple (LCM) of the given whole numbers. Among the options, 48 is the only number that could not be used as a common denominator. The correct answer is d) 48.

Step-by-step explanation:

Common denominators are required when adding or subtracting fractions. To find a common denominator, we need to identify the prime factors of each number and then determine the least common multiple (LCM). In this case, we need to find the LCM of the given whole numbers.

- a) 64:
`\(2^6\)`

- b) 72:
`\(2^3 * 3^2\)`

- c) 96:
`\(2^5 * 3\)`

- d) 48:
`\(2^4 * 3\)`

To find the LCM, we take the highest power of each prime factor involved. Therefore, the LCM is
`\(2^6 * 3^2\)`. Now, we can see that 48 is not a factor of this LCM, making it the only number that could not be used as a common denominator.

In conclusion, when adding fractions with denominators of 64, 72, and 96, we could use 48 as a common denominator. However, for the sake of efficiency and simplicity, it is often preferable to use the LCM to avoid dealing with unnecessarily large denominators.

Therefore, The correct answer is d) 48.