OBJ: To find the least common multiple of two numbers.

VocabularyMultiple- the product of the number and any

nonzero whole number. Common Multiple – a multiple that is shared

by two or more numbers. Least Common Multiple – the least of the

common multiples of two or more numbers. Least Common Denominator – the least

common multiple of the denominators. You can use the LCD to compare and order fractions.

Finding the LCMMethod 1

List the multiples of each number.

Identify the least number that is on both lists.

Example – Find the LCM of 16 and 24.

Method 2Find the common

factors of the numbers.

Multiply all of the factors, using each common factor only once.

Example – Find the LCM of 16 and 24.

Find the LCM of1. 20 and 252. 6, 8, and 203. 15, 30, 504. 15x2, 27x5. 6m2, 10m3

6. 14ab and 21bc7. 4g3h2 and 15g2h4

Least Common DenominatorWrite the fractions and simplify.Find the LCD of the fractions.Write the equivalent fractions using the LCD.Compare the numerators. Example – Find the LCD and compare the

fractions. 5/6, 7/95/8, 13/207/12, 11/155/16, 3/10

ExamplesOne brand of hot dogs is sold in packages of 6.

One brand of hot dog buns is sold in packages of 8. What is the least number of hot dogs Kimberly can buy and be able to buy an equal number of hot dog buns?

Last year a poll of 1200 students found that 300 spoke a first language other than English. This year a poll of 10,000 students found that 4000 students spoke a first language other than English. In which year was the fraction of non-English first language speakers greater?

How do you find the LCM of two or more numbers?

What is the least common multiple of three numbers that are relatively prime?