Question

Peter's Party Zone sells cups in packages of 6 and plates in packages of 8. Shaniya is hosting a birthday party for her little sister and wants to have the same number of each item. What is the least number of packages of plates Shaniya needs to buy?

Answer 1

Answer:

3

Step-by-step explanation:

lcm of 6 and 8 = 24

least number of packages of plates = 24/8 = 3

Answer 2

Answer:

4 packages of cups and 3 packages of plates should be bought to get same number of cups and plates.

Step-by-step explanation:

Given the number of cups in a package is 6.

The number of plates in a package is 8.

To get the same number of each item, we must find the least common multiple of both the numbers.

The least common multiple (LCM) of any two numbers is the lowest possible number that can be divisible by the numbers.

The prime factorization of 6: $2\times3$  or $2^1\times3^ 1$

The prime factorization of 18: $2\times2 \times2$ or $2^3$

In prime factorization method, the LCM is the product of the common and uncommon prime factors with the greatest exponent.

So, the LCM(6, 8) is $2^3\times 3^1=8\times 3=24$

Then the least packages of cups and plates should be

$\dfrac{24}{6} =4 ~~\mbox{and}~~\dfrac{24}{8} =3$

Therefore, 4 packages of cups and 3 packages of plates should be bought to get same number of cups and plates.

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