&KDSWHU5-3
Extend each list until you find a
multiple common to all the numbers.Least Common Multiple
Objective To find the least common multiple (LCM) of two or more numbers- To find the least common denominator (LCD) of two or more fractions
The high school’s soccer, field hockey, and baseball teams
all had games today. The soccer team plays every 6 days,
the field hockey team plays every 5 days, and the baseball
team plays every 3 days. How many days from now will
all three teams have games on the same day again?
To find the number of days from now that the teams
will play again on the same day, find the least common
multipleof 6, 5, and 3.
A is the product of a number and any whole
number. Multiples shared by two or more whole
numbers are. The least nonzero
common multiple of two or more numbers is their
.
Find the LCM of 3, 5, and 6.Method 1 List the Multiples- List the multiples of each number.
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30,...
Multiples of 5: 5, 10, 15, 20, 25, 30,...
Multiples of 6: 6, 12, 18, 24, 30,... - Identify the least multiple that is common to the three numbers: 30
So the LCM of 3, 5, and 6 is 30.
Method 2 Use Prime Factorization- Write the prime factorization of each composite number.
3 is prime.
5 is prime.
6 2 • 3 - Write each prime factor the greatest number of times it appears
in each of the prime factorizations. Then multiply the factors
to find the LCM.
2 • 3• 5 30
So the LCM of 3, 5, and 6 is 30.
The three teams will play again on the same day in 30 days.
The LCM of relatively prime numbers is their product.
What is the least common multiple of 3 and 5?
The LCM of 3 and 5 is 3 • 5, or 15.least common multiple (LCM)common multiplesmultiple