Least common multiple (lcm) & greatest
Download as PPTX, PDF2 likes5,803 views
This document discusses different methods for finding the least common multiple (LCM) of two or more numbers. It explains that the LCM is the smallest number that the given numbers will all divide into evenly. Then it describes four methods: multiplication, prime factorization, Venn diagrams, and using the greatest common factor (GCF). For each method it provides an example of finding the LCM of 24 and 18, and the answer is consistently 72.
Least common multiple (lcm) & greatest
- 1. C.E.T. Colegio Myrang 6th grade Math Mrs. Shiara Agosto
- 3. The LCM is the smallest number that two or more numbers will divide into evenly. It is the smallest non-zero multiple between two or more numbers. There are a couple of ways to find out the LCM: Multiplication Prime Factorization Using Venn Diagrams Using the GCF of the numbers. Least Common Multiple (LCM)
- 4. One of the ways to find the LCM is multiplication. With this method, you simply construct a list of the multiples of each number and find the smallest one that is present in both lists. 24: 24, 48, 72, 96, 108, 132 18: 18, 36, 54, 72, 90, 108 The LCM of 24 and 18 is 72. Multiplication
- 5. You can also use Prime Factorization to find the LCM. First, do the Prime Factorization of each number. Prime Factorization 24 4 3 2 8 2 2 18 3 36 2
- 6. Then, simply multiply the greater amount of each prime factor and the product of them will be the LCM. Align the prime factors so you can visualize. 2 x 2 x 2 x 3 = 24 2 x 3 x 3 = 18 The greatest number of 2s is 2x2x2 (in the PF of 24). The greatest number of 3s is 3x3 (in the PF of 18). So, to obtain the LCM of 24 and 18: 2 x 2 x 2 x 3 x 3 = 72 LCM of 24 and 18. Prime Factorization
- 7. Using Venn Diagrams To use Venn Diagrams with Prime Factorization, put the repeating factors in the middle and then the remaining factors in each corresponding circle. Then multiply. 24 18 2 2 2 3 3 2 x 2 x 2 x 3 x 3 = 72
- 8. Find the GFC of both numbers by listing its factors (the numbers it can be divided into evenly). The GFC is the biggest number that appears in both lists. 24: 1, 2, 3, 4, 6, 8, 12, 24 18: 1, 2, 3, 6, 9, 18 GCF = 6 Divide one of the numbers by the GFC and then multiply the answer with the other number. 24 ÷ 6 = 4 ; 18 x 4 = 72 LCM 18 ÷ 6 = 3 ; 24 x 3 = 72 LCM Using Greatest Common Factor (GFC)