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  • Least Common Denominator Calculator

Least Common Denominator Calculator

Enter Values
w1= n1= d1=
w2= n2= d2=
w3= n3= d3=
wn{w}_{n} - A whole number (or leave it empty)
nn{n}_{n} - Numerator of the fraction
dn{d}_{n} - Denominator of the fraction
by Publicalculator.com

Result

LCD: 105
(Least Common Denominator)

Equivalent fractions to the given are:

\(4\frac{5}{7}\) = \(\frac{33}{7}\) = \(\frac{495}{105}\)

\(\frac{9}{15}\) = \(\frac{63}{105}\)

\(\frac{3}{3}\) = \(\frac{105}{105}\)


Use this Least Common Denominator Calculator (LCD) to work out up to 7 fractions and mixed numbers simultaneously. The whole number should be added as a simple fraction, e.g. 4/1 for whole number 4, etc. If you added a fraction that you no longer need, just leave all the cells blank and carry on with the rest of the calculation.

What is the Least Common Denominator (LCD)?

The Least Common Denominator (LCD) is the smallest number that is a common multiple of the denominators of two or more fractions. It is used to compare, add, or subtract fractions by rewriting them with the same denominator. This process is crucial because fractions with the same denominator are easier to manipulate mathematically.

Example 1:

For fractions 14 and 16, the LCD is 12.\text{For fractions } \frac{1}{4} \text{ and } \frac{1}{6}, \text{ the LCD is } 12.

How to Find the Lowest Common Denominator?

To find the LCD of the number of fractions, mixed or whole numbers, for each of them the denominator must be determined first. It's fair mainly when you are working out around mixed and whole numbers - they all have to be converted to improper fractions. When having all the denominators, the Lowest Common Multiple (LCM) of them has to be found. When the result of LCM will be known, all the numerators of the corresponding fractions should be adjusted to get the given fractions rewritten with the equivalent fractions.

For the aforementioned Example 1, the multiples of each denominator can be listed:

For 4: 4,8,12,16,…

For 6: 6,12,18,24,…

Finding, among the lists above, the Lowest Common Multiple (LCM), which stands as the smallest number present in both lists, leads to the answer. In this case, LCM is 12, ensuring it divides evenly by each denominator.

There are some advanced methods of determining LCD. Along with the Greatest Common Factor (GCF), which is the one of the methods, there is the Prime Factorization Method. Finding Least Common Denominator using Prime Factorization Method is shown below as an example:

Example Fractions: 38\frac{3}{8} and 512\frac{5}{12}

  • Denominators: 88 and 1212.

Find the Prime Factorization:

  • 8=2×2×2=238 = 2 \times 2 \times 2 = 2^3,
  • 12=2×2×3=22×312 = 2 \times 2 \times 3 = 2^2 \times 3.

Take the Highest Power of Each Prime Number:

  • From 88: 232^3,
  • From 1212: 313^1,
  • LCD = 23×3=242^3 \times 3 = 24.

Rewrite the Fractions with the LCD:

  • Multiply both numerator and denominator by the necessary factor to match the LCD.
38=3×38×3=924,512=5×212×2=1024.\frac{3}{8} = \frac{3 \times 3}{8 \times 3} = \frac{9}{24}, \quad \frac{5}{12} = \frac{5 \times 2}{12 \times 2} = \frac{10}{24}.

Result: Both fractions are now expressed with the denominator 2424: 924\frac{9}{24} and 1024\frac{10}{24}.


Sources:

Larson, R., Hostetler, R.P., & Edwards, B.H. (2013). Algebra and Trigonometry: A Functions Approach. Brooks/Cole Cengage Learning.

Keedy, M.L., & Bittinger, M.L. (1982). Algebra and Trigonometry: A Functions Approach. Addison Wesley Publishing Company.


Cite as followed:
Zemtsov, I. "Least Common Denominator Calculator". Publicalculator.com, 02 January 2025. Published at: https://publicalculator.com/lcd-calculator. Accessed: Jan 22, 2025.