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By finding the lowest common multiple of the denominators.
By finding the lowest common multiple of the fractions with different denomiators that need to be added or subtracted
The LCD of 1/4 and 1/6 is 12
You don't normally calculate the lcd of a single number (fraction). You would normally take the lcd of two or more fractions. In that case, ONLY the denominators are relevant to find the lcd.
You can find a common denominator without factoring but it will not be the least such number. That means that you will end up working with numbers that are far larger than they need be. For example, 5/12 + 7/18 Using LCD = 36: 15/36 + 14/36 = 29/36 Without LCD : 90/216 + 84/216 = 174/216 which can then be simplified to 29/36.