GCF & LCM - Pre Algebra

1. What is the GCF of $12$ and $18$?

   $6$. It is the largest number that divides both.

2. What is the greatest common factor (GCF) of two whole numbers?

   The largest whole number that is a factor of both numbers.

3. What is the LCM of $4$ and $6$?

   $12$. It is the first number in both lists of multiples.

4. What is the GCF of $15$ and $45$?

   $15$. Since $15$ divides $45$, the smaller number is the GCF.

5. Hot dogs come in packs of $10$ and buns in packs of $8$. What is the smallest equal number of each you can buy?

   $40$ (4 packs of hot dogs and 5 packs of buns). This is the LCM of $10$ and $8$.

6. What is the LCM of $8$ and $12$?

   $24$. The multiples of $12$ are $12, 24$, and $24$ is the first one divisible by $8$.

7. What is the GCF of $7$ and $20$?

   $1$. They share no factor other than $1$.

8. What is the greatest number of identical bags that can hold $18$ apples and $24$ oranges with none left over?

   $6$ bags, each with $3$ apples and $4$ oranges. This is the GCF of $18$ and $24$.

9. For two positive whole numbers, how are their GCF and LCM related to their product?

   GCF $\times$ LCM equals the product of the two numbers.

10. What is the least common multiple (LCM) of two whole numbers?

    The smallest positive number that is a multiple of both numbers.

11. What is the GCF of $24$ and $36$?

    $12$. Since $24 = 12 \cdot 2$ and $36 = 12 \cdot 3$, and $2$ and $3$ share no factor.

12. What is the LCM of $5$ and $9$?

    $45$. Their GCF is $1$, so the LCM is their product.

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