2The greatest common factor (GCF) of 2 or more numbers is the largest number that can divide into all of the numbers. Find the GCF of 42 and 60. Write the prime factorization of each number.
3Find the GCF of 42 and 60.1What prime factors do the numbers have in common? Multiply those numbers with the lowest exponents . The GCF is 2 x 3 = 6 6 is the largest number that can go into 42 and 60!
5Greatest Common Factor Find the GCF of12 and 1818 and 2724 and 3036 and 4524 and 3616, 32 and 4018,27 and 36
6Find the GCF of :2x3x5 and 2x3x72x3x5x7 and 2x2x3x113) 2x2x3x5 and 2x2x3x114) 2x2x2x5x7 and 2x2x2x5x115) 2x2x2x7x7 and 2x2x2x7x11
7GCF Example: Applying what we have learned… Samantha has two pieces of cloth. One piece is 72 inches wide and the other piece is 90 inches wide. She wants to cut both pieces into strips of equal width that are as wide as possible. How wide should she cut the strips?2 l l 902 l l 452 l l 153 l l 53 l172 = 2 x 2 x 2 x 3 x 390 = 2 x 3 x 3 x 5GCF = 2 x 3 x 3 = 18Samantha should cut each piece to be 18 inches wide
8YOUR TURN!1. Mrs. Evans has 120 crayons and 30 pieces of paper to give to her students. What is the largest # of students she can have in her class so that each student gets equal # of crayons and equal # of paper. 2. I am planting 50 apple trees and 30 peach trees. I want the same number and type of trees per row. What is the maximum number of trees I can plant per row?
10The least common multiple of 2 or more numbers is the smallest number that is common between two lists of multiples.
11Write the common and non common factors with the greatest exponents Find the LCM of 42 and 60.1Write the common and non common factors with the greatest exponentsThe LCM of 42 and 60 is 420.
12Find the least common multiple (LCM). Method 2: Use a list.3, 4, and 93: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, . . .List multiples of 3, 4, and 9.4: 4, 8, 12, 16, 20, 24, 28, 32, 36, …Find the smallest number that is in all the lists.9: 9, 18, 27, 36, 45, . . .The least common multiple of 3, 4, and 9 is 36.
13Least Common MultipleFind the LCM of the following2 and 53 and 82, 3 and 44. 3 and 95. 2,4 and 6
141. 2x5 and 5x5 2. 2x2x3 and 2x2x5 3. 2x2x3 and 2x7 4.2x2x2 and 2x7 Find the LCM of1. 2x5 and 5x52. 2x2x3 and 2x2x53. 2x2x3 and 2x74.2x2x2 and 2x75. 2x2x5 and 5x5
15LCM Example: Applying what we have learned… Ben exercises every 12 days and Isabel every 8 days. Ben and Isabel both exercised today. How many days will it be until they exercise together again?2 l l 82 l l 43 l l 212 = 2 x 2 x 38 = 2 x 2 x 2LCM = 2 x 2 x 2 x 3 = 24Ben and Isabel would exercise on the same day every 24 days.
16YOUR TURN1.Two bikers are riding a circular path. The first rider completes a round in 12 minutes. The second rider completes a round in 18 minutes. If they both started at the same place and time and go in the same direction, after how many minutes will they meet again at the starting point?2. Sean has 8-inch pieces of toy train track and Ruth has 18-inch pieces of train track. How many of each piece would each child need to build tracks that are equal in length?