find a common denominator: 4/7 and 5/8
To find a common denominator for 4/7 and 5/8, we need to find the least common multiple (LCM) of the denominators 7 and 8.
The prime factorization of 7 is 7, and the prime factorization of 8 is 2 x 2 x 2.
To find the LCM, we include the highest power of each prime factor:
7 x 2 x 2 x 2 = 56
Therefore, the common denominator for 4/7 and 5/8 is 56.
To find a common denominator for fractions, you need to find the smallest multiple that both denominators share.
In this case, the denominators are 7 and 8.
To find the least common multiple (LCM) of 7 and 8, you can list the multiples of each number and look for the smallest common multiple.
Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, ...
Multiples of 8: 8, 16, 24, 32, 40, 48, 56, ...
From the list above, we see that 56 is the smallest common multiple of 7 and 8.
Therefore, the common denominator for the fractions 4/7 and 5/8 is 56.