10 Questions
What is the definition of the least common multiple (LCM)?
The smallest positive multiple that two or more numbers share
What is the greatest common factor (GCF) used for?
To simplify expressions and find the LCM
What are multiples?
Numbers from the times table that are obtained by multiplying a number by an integer
What is the proper term for the least common multiple (LCM)?
Least common multiple (LCM)
What method uses lists of multiples of each number to find the least common multiple?
$Listing$ $Multiples$
What is the least common multiple (LCM)?
The smallest number that can be evenly divided by multiple numbers without leaving a remainder
How is the greatest common factor (GCF) related to finding the LCM?
The LCM is obtained by multiplying the numbers together and then dividing by the GCF
What method involves identifying prime factors to find the LCM?
Prime factorization method
In prime factorization, what are multiplied together to find the LCM?
Prime factors with the highest exponents from each number
How does the listing method find the LCM?
$LCM = \text{Common Multiple}$
Study Notes
- The least common multiple (LCM) is the smallest number that can be evenly divided by multiple numbers without leaving a remainder.
- To find the LCM of two numbers, one can compile a list of their multiples until a common multiple is found, or find the greatest common factor (GCF) and multiply the numbers together, then divide by the GCF.
- Factors of each number are identified to find the GCF. The largest factor shared by both numbers is the GCF.
- Another method to find the LCM is through prime factorization. Prime factors are identified for each number, then the factors with the highest exponents are multiplied together to find the LCM.
- The LCM can be found by keeping the prime factors with the highest exponents, regardless of which number they come from, and then multiplying them together.
- The process for finding the LCM can be demonstrated through examples involving the listing method, GCF division method, and prime factorization method.
- The listing method involves creating a list of multiples for each number until a common multiple is found, while the GCF division method uses the formula of multiplying the numbers together and then dividing by the GCF to find the LCM.
- The prime factorization method requires the breakdown of factors to only prime numbers, comparing the prime factors, and then multiplying the prime factors with the highest exponents to find the LCM.
- Examples of the LCM include finding the LCM of 4 and 6 using the listing method, 4 and 6 using the GCF division method, and 4, 9, and 3 using the prime factorization method.
Test your knowledge of the concept of least common multiple (LCM) and its applications in adding and subtracting fractions and finding equal quantities. Understand the definition of LCM as the smallest positive multiple shared by two or more numbers.
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