Definitions:
•Least Common Multiple (L.C.M.) – The smallest natural number that is divisible
by all the given numbers
•Least Common Denominator (L.C.D.) – The least common multiple of the
denominators
Objective 1: Find the L.C.M. by listing
•To find the L.C.M. by listing
o List multiples of the greatest (biggest) number until you find a
multiple that is divisible by all the other given numbers
o Find the L.C.M. of 36 and 120 by listing
Objective 2: Find the L.C.M. using prime
factorization
•Find the L.C.M. using prime factorization:
o Write the prime factorization of each given number
o Write a factorization that contains each prime factor the greatest
amount of times it occurs in either factor tree
o Multiply to get the L.C.M.
o Find the L.C.M. of 36 and 120 using prime factorization
o Find the L.C.M. of 24, 90, and 70 using prime factorization
Objective 3: Find the L.C.M of a set of monomials
•To find the L.C.M of a group of monomials , we use the
prime factorization method and treat the variables as if they were primes
o Find the L.C.M. of 
Objective 4: Write fractions as equivalent
fractions with the L.C.D.
•To write fractions as equivalent fractions with the L.C.D.
o Find the L.C.M. of the two denominators
o Take the L.C.M. and divide by each respective denominator
o Multiply each answer by the respective numerator to come up with the new
numerator of each fraction
o Find the L.C.D. of 
o Find the L.C.D. of 
Objective 5: Write rational expressions as
equivalent ex pressions with the L .C.D.
• Rational expressions are rewritten in the same way as numeric fractions
o Find the L.C.D. of 
