Question

choose two numbers from this list; 3,4,6,12. explain the difference between finding the greatest common factor and the least common multiple of the two numbers.Rewrite the expression as a product using the GCF and distributive property.explain your answer. 27+45=_______

Answer 1

Let us pick the numbers 3, and 4 and work with them for illustration.

The Greatest Common Factor (GCF) of two or numbers is the greatest factor that is common to all of the numbers listed.

The GCF of 3, and 4 is found by asking ourselves the question "What is the greatest integer that is a factor of 3 but also a factor of 4? "

The answer is 1 because 3 / 1 = 3 and 4 / 1 = 4 and they are is not greater number than 1 that gives an integer upon division for 3 and 4.

The Least Common Multiple (LCM) of two or more numbers is the least number that is divisible by all of the numbers listed.

To find LCM of 3 and 4, we have to ask ourselves "what is the least numbers that can be divided into both 3 and 4? "

The LCM of 3 and 4 is 12. No other number lower than 12 satisfies the conditions of an LCM.

Question.6

To write the expression as a product, we first need to find the GCF of 27 and 45.

The factors of 27 are

`\begin{gathered} 27=3\cdot3\cdot3 \\ 27=9\cdot3 \end{gathered}`

and the factors of 45 are

`\begin{gathered} 45=9\cdot5 \\ 45=3\cdot3\cdot5 \end{gathered}`

We see that the factor common to 27 and 45 is 9; therefore the expression 27 + 45 can be written as

`27+45=(9\cdot3)+(9\cdot5)`

Factoring out 9 gives