They are essentially the same. A common denominator is the common multiple of a set of denominators of a set of fractions.
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Common denominators are common multiples that are being used as denominators.
The least common denominator is the least common multiple of the denominators of the fractions.
Common denominators are multiples that are being used as denominators. The process to find them is the same.
The least common denominator is the least common multiple of the denominators.
Both result from the comparison of integers. The process used to find them is the same. The only difference is in their function. One is a denominator, one isn't.