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```5.2. COUNTING FACTORS, GREATEST COMMON FACTOR, AND LEAST COMMON MULTIPLE
87
Build-Up Method
Example. Find LCM(36, 60).
(1) Factor each number into primes.
36 = 22 · 32
60 = 22 · 3 · 5
(2) Start with one number’s prime factorization, say 36, and compare its prime
factorization to the prime factorization of the other number, 60 in this case.
We begin with
22 · 32.
Comparing with the prime factors of 60, there is no need to increase the exponents of 2 or 3. We simply need to add a factor of 5.
LCM(36, 60) = 22 ·2 ·5 = 180.
Example. Find GCF(90, 36, 54) and LCM(90, 36, 54).
90 = 2 · 32 · 5
36 = 22 · 32
54 = 2 · 33
GCF(90, 36, 54) = 2 · 32 = 18
Note.
LCM(90, 36, 54) = 22 · 33 · 5 = 4 · 27 · 5 = 540
GCF(36, 60) = 12 and LCM(36, 60) = 180.
12 · 180 = 2160 and 36 · 60 = 2160.
This is an instance of
Theorem. Let a and b be any two whole numbers. Then
GCF(a, b) ⇥ LCM(a, b) = ab.
```