LCM from Prime Factors
Part of the Factors & Fractions section of Coddy's Pre-Algebra journey. Lesson 15 of 58.
Primes give the LCM too. Factor both numbers: 20 is 2^2 × 5 and 30 is 2 × 3 × 5. A multiple of 20 must contain two 2s and a 5, and a multiple of 30 must contain a 2, a 3 and a 5. The smallest number containing all of that takes each prime as many times as the number that needs it most.
That is two 2s, one 3 and one 5: 2^2 × 3 × 5 is 60. So the LCM of 20 and 30 is 60. Check it: 60 / 20 is 3 and 60 / 30 is 2.
Compare it with the GCF. The GCF keeps only the shared primes, each with its smaller exponent. The LCM keeps every prime that appears, each with its larger exponent. One trims down to what both have; the other builds up to what either needs.
Challenge
Find the least common multiple L of 12 and 18 using prime factorizations. Write L equal to the product of the primes it needs, then work it out on the next line.
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
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 LCM