"Common" means "same for both". There's nothing common about one single
number. When you have at least two numbers, then you can start looking for
things that are common to both of them.
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60 is the least common denominator of 3 4 5 6 10 and 15.
60
If that's 5/6 and 10/50, the least common denominator is 150. But since 10/50 = 1/5, the least common denominator is 30.
I do it by finding a common denominator. For example, 2/3 - 1/5. The least common denominator is 15. 2/3 = 10/15, and 1/5 = 3/15, the difference of which is 7/15. Here is another example: 5/6 - 2/3. In this case, the least common denominator is 6. 2/3 = 4/6, and 5/6 - 4/6 = 1/6.
There is none because the Least Common Denominator (or LCD) is the Least Common Multiple (LCM) of the denominators of a pair of fractions.