Section 1.8 - The Least Common Multiple and the Greatest Common Factor

Explain how to find the GCF of 8 and 28 using prime factorization

1-Prime factor each number 2-Identify the common prime factors. 3-The GCF is a product of all the common prime factors found in step-2, If there are no common prime factors, the GCF is 1.

Explain how to find the LCM of 8 and 28 using prime factorization

1-Prime factor each number 2-The LCM is a product of prime factors, where each factor is used the greatest number of times that it appears in any one factorization.

Ways to find LCM (The least common multiples of numbers)

Listing Multiples Using Prime Factorization

To find the greatest common factor of two (or more) whole numbers:

1. Prime factor each number. 2. Identify the common prime factors. 3. The GCF is a product of all the common prime factors found in Step 2. If there are no common prime factors, the GCF is 1

Finding the LCM Using Prime Factorization To find the least common multiple of two (or more) whole numbers:

1. Prime factor each number. 2. The LCM is a product of prime factors, where each factor is used the greatest number of times it appears in any one factorization.

Finding the LCM by Listing the Multiples of the Largest Number To find the least common multiple of two (or more) whole numbers:

1. Write multiples of the largest number by multiplying it by and so on. 2. Continue this process until you find the first multiple of the larger number that is divisible by each of the smaller numbers. That multiple is their LCM

florist

A dealer in flowers. someone who grows and deals in flowers someone who sells flowers and other plants a shop where flowers and ornamental plants are sold

abbreviation

A shortened form of a word or phrase a shortened form of a word a short form of a word or expression

If there are no common prime factors, the GCF is 1

GCF(8,15)= 1 Prime factors of 8 and 15 are: 8=2.2.2 15=3.5 They have no common factors, so GCF of them is 1.

GCF

Greatest Common Factor The greatest number that is a factor of each of two or more numbers. The highest number that divides exactly into two or more numbers

How can you tell by looking at the prime factorizations of two whole numbers that their GCF is 1?

If they have no prime factors in common, their GCF (also called GCD = Greatest Common Divisor) is 1.

LCM

Least Common Multiple The least number that is a common multiple of 2 or more numbers the smallest multiple of two (or more) numbers (the smallest number that is a multiple of both)

The prime factorization of 12 is and the prime factorization of 15 is Explain why the LCM of 12 and 15 is not 2.2.3.3.5

Since each factor has only one factor 3, the LCM should only have one 3.

least common multiple

The least common multiple of two whole numbers is the smallest common multiple of the numbers. ---- The smallest multiple (other than zero) that two or more numbers have in common. LCM. The smallest common multiple of a set of two or more numbers. The smallest positive number that is a multiple of two or more numbers.

multiples

The multiples of a number are the products of that number and and so on. 1, 2, 3, 4, 5, --- a product of a whole number and any other whole number the product of two factors a number that can be divided by another number without a remainder

common multiple

a number that is a multiple of two or more numbers a number into which each number in a given set may be evenly divided.

ladles

a spoon with a long handle and a bowl shaped like a cup 1 oz = 1/8 cup

Bouquets

bunches of flowers A bunch of flowers

BIORHYTHMS

cyclic phenomena that occur with established regularity in living organisms

One number is ____by another if, when dividing them, we get a remainder of 0

divisible is the result with the remainder of 0

identical

exactly the same exactly the same, alike in every way exactly the same, or very similar

The least common multiple (LCM) of two whole numbers? ex: 12 is a multiple of 3 and 4 ( because 12 is divisible by both 3 and 4).

is the smallest whole number that is divisible by both of those numbers.

lengthy

long being very long in distance or time very long (a) long in time, duration, or distance 長的 long in time or size

The ____ of a number are the products of that number and and so on

multiples

arrangements

plans made beforehand; preparations

rhythms

repetitive, cyclical patterns of behavior repetition, positive/negative, part to whole comparison

In general, the LCM of two whole numbers is the ___whole number that is divisible by both numbers

smallest

instructed

taught taught or trained He ________ the students to make sure they completed the homework before 5pm tomorrow.

The greatest common factor(GCF) of two whole numbers is 26=1,2,...,13,...26. 39=1,...,3,13,...,....,39 GCF(26,39)=13.

the largest common factor of the numbers

blood pressure

the pressure that is exerted by the blood against the walls of blood vessels The pressure of circulating blood against the walls of the arteries. the amount of force exerted against the walls of an artery by the blood

tiresome

tiring; boring; annoying boring causing one to feel bored or annoyed

critical zone

very important something of great importance extremely important being important to the outcome of a situation