By Eric Benac
Updated Aug 30, 2022
Adding decimal numbers together requires a common denominator, which you can only obtain after converting each decimal to a fraction. This guide walks you through a reliable, step‑by‑step method that works for any number of decimals.
Write a horizontal dash below the decimal point and place a 1 directly beneath the dash. For example, 0.75 becomes 0.75/1. The numerator is the number above the dash; the denominator is the 1.
Multiply both the numerator and denominator by the appropriate power of ten that removes the decimal point. 0.75/1 becomes 75/100. Repeat for every decimal.
Reduce each fraction by dividing numerator and denominator by their greatest common divisor. For instance, 75/100 simplifies to 3/4 after dividing by 25. Continue until no further reduction is possible.
Write the denominator of each simplified fraction in a vertical list. Ignore the numerators for the next steps. Example: if your fractions are 1/5, 1/6 and 1/15, list 5, 6, and 15.
Using a calculator, produce the first few multiples (up to 10×) for each denominator and record them next to the corresponding number.
Scan the lists of multiples to identify the smallest number that appears in all three. That number is the least common denominator. In the example, 5, 6, and 15 share 30 as the smallest common multiple.
Divide the LCM by each original denominator to obtain the factor needed for each fraction. For 30 ÷ 5 = 6, 30 ÷ 6 = 5, and 30 ÷ 15 = 2. Write these factors beside the corresponding simplified fractions.
Multiply each fraction’s numerator by its conversion factor. Using the example: 1×6 = 6, 1×5 = 5, and 1×2 = 2.
Write the new numerators over the common denominator: 6/30, 5/30, and 2/30. Add the numerators to get 13/30. If possible, simplify the result; here, 13 is prime, so 13/30 is already in lowest terms.
By following these nine steps, you can confidently find the least common denominator for any set of decimal numbers.
