How are a common denominator and a common multiple alike and different.

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The Common Denominator is the bottom part of a fraction which has been matched to 2 or more fractions. For example 1/2 + 1/4 is easier if you use 2/4 + 1/4 = 3/4. You can also use it for 3/5 + 1 2/3 Becomes 3/5 + 5/3 (Improper fraction) and you change that to 9/15 + 25/15 = 34/15 = 2 4/15

A common denominator is a shared denominator in two or several fractions. So 2/5 and 1/5 have common denominators. A denominator is the bottom number of a fraction while a numerator is the top.
A common multiple is a number that is a multiple of each or more numbers.
20 & 10 share the common multiple 5. 60 & 36 share the common multiple of 12. A number can have more than one common multiple.