Presentation on theme: "EXAMPLE 1 Finding the Least Common Multiple"— Presentation transcript:
1EXAMPLE 1Finding the Least Common MultipleA veterinarian at an animal clinic is on call every four days. Today is Saturday, and the veterinarian is on call. In how many more days will the veterinarian be on call on a Saturday again?Animal ClinicSOLUTIONThe veterinarian is on call every 4 days. A Saturday occurs every 7 days. Find the least common multiple of 4 and 7.
2EXAMPLE 1Finding the Least Common MultipleUse a calendar. Start with a Saturday and circle every 4 days on a calendar. You can see that the veterinarian will be on call on a Saturday in 28 days.METHOD 1
3EXAMPLE 1Finding the Least Common MultipleMETHOD 2Make a list.List the multiples of each number.Multiples of 4:4, 8, 12, 16, 20, 24, 28, 32, . . .Multiples of 7:7, 14, 21, 28, 35, 42, 49, 56, . . .The least common multiple is the first number that appears in both lists. The LCM of 4 and 7 is 28.
4EXAMPLE 1Finding the Least Common MultipleMETHOD 3Use prime factorization.Write the prime factorization of each number.4= 227= 7Circle the greatest power of each prime factor.4= 227= 7The LCM of 4 and 7 is the product of the circled numbers:= 28
5EXAMPLE 1Finding the Least Common MultipleIn 28 days, the veterinarian will be on call on a Saturday.ANSWER
6EXAMPLE 2Finding the Least Common MultipleFind the LCM of 32, 96, and 120 using prime factorization.SOLUTIONWrite the prime factorization of each number and circle the greatest power of each prime factor.STEP 132= 2596=120=
7EXAMPLE 2Finding the Least Common MultipleSTEP 2Find the product of the circled factors.= 480The LCM of 32, 96, and 120 is 480.ANSWER
8EXAMPLE 3Finding the LCM of MonomialsFind the LCM of 6x2y and 9x4z.SOLUTIONFactor each expression using exponents and circle the greatest power of each factor.STEP 16x2y = x2 y9x4z = 32 x4 zFind the product of the circled factors.STEP 2x4 y z = 18x4yz
9EXAMPLE 3Finding the LCM of MonomialsThe LCM of 6x2y and 9x4z is 18x4yz.ANSWER
10GUIDED PRACTICEfor Examples 1,2 and 31. What If? In Example 1, suppose the veterinarian is on call every 3 days. In how many more days will the vet be on call on a Saturday again?In 21 days, the veterinarian will be on call on a Saturday.ANSWER
11GUIDED PRACTICEfor Examples 1,2 and 3Find the least common multiple of the numbers., 15
12GUIDED PRACTICEfor Examples 1,2 and 3The LCM of 6 and 15 is 30.ANSWER