Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
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.