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Find the Least Common Denominator (LCD) of fractions with step-by-step solutions using prime factorization.
The Least Common Denominator (LCD) is the smallest number that is a multiple of all the denominators in a set of fractions. It's essential for adding, subtracting, and comparing fractions with different denominators.
Example: LCD(4,6) = 2² × 3 = 12
Example: Multiples of 4: 4,8,12,16... Multiples of 6: 6,12,18... LCD = 12
You need a common denominator to add fractions. Using the LCD keeps numbers small and simplifies calculations.
Converting to LCD makes it easy to compare fractions - just look at the numerators.
Using LCD instead of any common denominator means smaller numbers and less simplifying later.
LCD (Least Common Denominator) and LCM (Least Common Multiple) are the same thing! LCD is just the term we use specifically when working with fractions. The LCD of denominators is the LCM of those same numbers.
Yes, you can use any common multiple of the denominators. However, using the LCD keeps your numbers smaller and makes the math easier. You'll have less simplifying to do at the end.
Find the LCM of the first two denominators, then find the LCM of that result and the third denominator, and so on. Or use prime factorization for all denominators at once and take the highest power of each prime factor.
The larger denominator is automatically the LCD. For example, if you have denominators 4 and 12, the LCD is 12 because 12 is a multiple of 4.
Divide the LCD by each original denominator to find the multiplier. Then multiply both the numerator and denominator of each fraction by its multiplier. This creates equivalent fractions with the LCD.
The LCD of two prime numbers is simply their product. For example, LCD(3,5) = 15. Prime numbers have no common factors except 1, so their LCM is their product.