Least Common Multiple

What is a multiple? A multiple of a whole number is the product of the whole number and any number Example the multiples of 8 are 8 x 1 = 8 8 x 2 = 16 8 x 3 = 24 8 x 4 = 32

What are the multiples of 5?

What are the multiples of 8?

What is a LCM? LCM is the smallest number other than 0 that is a multiple of 2 or more whole numbers

Find the LCM by making a list List all the nonzero multiples 9: 9, 18, 27, 36, 45, 54, 63, 72 12: 12, 24, 36, 48, 60, 72 Identify the LCM from the list The LCM of 9 and 12 is 36.

HINTS The LCM cannot be larger than the product of the two whole numbers. The LCM of 3 and 4 cannot be larger than 12 because 3 x 4 = 12 Use your multiplication chart to help find the multiples

A quick review What is prime factorization? A composite number expressed as a product of primes Factor Trees 15 3 5

Find the LCM by using prime factorization Find the LCM of 15 and 25 15 25 5 3 5 5

15 and 25 cont. Identify common factors 15: 3, 5 25: 5, 5 Find the product of the common and remaining factors 3 x 5 x 5 = 75

School Dance Team The school dance team lines up in even rows of 3, 4, or 5 at practice. What is the least number of people needed to line up in rows or 3, 4, or 5?

To find the number of members needed you find the LCM for 3, 4 or 5

Use the list method

Using prime factorization

Fruit word problem Jessica is filling bags of fruit. She fills one bag with just apples, a second bag with just oranges, and a third bag with just pears. If each apple weighs 6 ounces, each orange weighs 8 ounces, and each pear weighs 9 ounces, at what point will each of the bags have the same weight?

List Method

Prime Factorization

The bags will have the same weight at 2  2  2  3  3 or 72 ounces.  

On a calculator TI 34 II 2nd key ) (math) Arrow over to lcm Enter key Enter 1st number Division key (,) Enter 2nd number ) TI 34 II Multiview Math key Enter Enter 1st number 2nd key . (,) Enter 2nd number )