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LCM and GCF

least common multiple – smallest number that 2 numbers will divide into

greatest common factor – biggest number that will divide into 2 numbers

– First step is to find prime factorizations for each value

Find the LCM + GCF for 27 and 90.

$27=3\times3\times3\ \ \ \ \ \ 90=2\times3\times3\times5$

$LCM=2\times3\times3\times3\times5=270$

$GCF=3\times3=9$

LCM = product of all factors

GCF = product of shared factors

When adding/subtracting factors, LCM will be common denominator.

$\frac{5}{12}+\frac{7}{18}=\ ?$

$(\frac{5}{12}\times\frac{3}{3})+(\frac{7}{18}\times\frac{2}{2})=\ ?$

$\frac{15}{36}+\frac{14}{36}=\frac{29}{36}$

LCM=2•2•3•3=36