Glossary
least common denominator
The least common denominator is the smallest number that both denominators divide into evenly, and it is the shared bottom number used to add or subtract fractions.
The least common denominator is the smallest number that every denominator in the problem divides into evenly. To add 1/4 and 1/6 it is 12, because 12 is the first number both 4 and 6 go into; you could use 24 and get the same answer after reducing, but 12 keeps the numbers small and the arithmetic easier to check. Find it by listing multiples of the larger denominator, or by taking the prime factors of each and keeping the highest power of every factor. Then rewrite each fraction with the new bottom number — multiply top and bottom by the same value, which changes the fraction's appearance and not its size — and add the numerators. In dosage work this step appears whenever a calculation mixes fractions, and it is where a wrongly scaled numerator produces an answer that is off by a clean factor.
Taught in
Related terms
- denominator — The denominator is the bottom number of a fraction: how many equal parts the whole is divided into, and therefore the size of each part.
- numerator — The numerator is the top number of a fraction: how many of the equal parts named by the denominator are being counted.
- mixed number — A mixed number combines a whole number and a proper fraction, such as 1 1/2, and is converted to an improper fraction before multiplying or dividing.
Source: The math guides in this course (ratio and proportion, measurement and conversion, dosage calculation): every definition and worked value above was written for this course, because arithmetic and unit conversion are not a publisher's prose, and each guide shows the method worked. Elsevier's own HESI A2 page, which names math among the areas the exam covers, is the exam-side source. (Elsevier HESI A2 page accessed 2026-10-23; definitions written 2026-10-27)