The Least Common Denominator
Part of the Factors & Fractions section of Coddy's Pre-Algebra journey. Lesson 31 of 58.
Any common multiple works as a denominator, but the smallest one keeps the numbers small. Take 5/6 + 1/8. The product 6 × 8, which is 48, works: 40/48 + 6/48 is 46/48, and that still has to be simplified to 23/24.
The least common multiple of 6 and 8 is 24. With it, 20/24 + 3/24 is 23/24 straight away, already in lowest terms. The LCM of the denominators is called the least common denominator, or LCD. It is the same LCM you found earlier in this section.
A quick way to find it: list the multiples of the bigger denominator until you reach one that the smaller denominator divides. Multiples of 8 are 8, 16, 24. 6 divides neither 8 nor 16, but it divides 24, so 24 is the LCD.
Challenge
Work out 3/10 + 4/15 over the least common denominator.
Try it yourself
Simplify the expression
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Factors & Fractions
1Factors and Multiples
What a Factor IsFactor PairsDivisibility RulesMultiplesPrime or CompositeRecap: Factors and Multiples4What a Fraction Is
Parts of a WholeFractions on the LineA Fraction of a NumberImproper FractionsRecap: What a Fraction Is7Multiplying Fractions
Top Times TopCancel FirstWhole Times FractionA Fraction of a FractionRecap: Multiplying Fractions10Fractions in Stories
Part of a GroupWhat Is LeftSharing a FractionScaling a RecipeRecap: Fraction Stories2Prime Factorization
Factor TreesUsing ExponentsOne Tree per NumberBigger NumbersRecap: Prime Factorization5Equivalent Fractions
Same Amount, New NameSimplifying FractionsSimplify in StepsComparing FractionsRecap: Equivalent Fractions3GCF and LCM
Greatest Common FactorGCF from Prime FactorsLeast Common MultipleLCM from Prime FactorsGCF or LCM?Recap: GCF and LCM6Adding and Subtracting
Same DenominatorDifferent DenominatorsSubtracting FractionsThe Least Common DenominatorNegative ResultsRecap: Adding and Subtracting