How are common denominator and a common multiple alike and different

East common multiple is the smallest multiple both numbers can go into. (Example: the LCM of 10 and 4 is 20, because both 10 and 4 go into 20 and 20 is the smallest number both 10 and 4 can go into. You could just multiply them both, but you'd get 40 and since its a bigger number it would be harder to work with.)

Least common denominator is just the least common multiple as a denominator. (Example: if you wanted to find the LCD of 5/7 and 1/10, you'd have to find the LCM of the demoniators (7 and 10) and then just use that as the denominator when adding fractions with unlikely denominators.) Sorry for such a long answer :P