IXL | GCF and LCM: word problems

Kelsey is stocking bathrooms at the hotel where she works. She has 12 rolls of toilet paper and 16 soaps. If she wants all bathrooms to be stocked identically, with the same combination of supplies in each one and nothing left over, what is the greatest number of bathrooms Kelsey can stock?

bathrooms

ref_doc_title.

Learn with an example

question

A family is preparing backpacks filled with school supplies to donate to children in need. They have 6 pencils and 15 notebooks. If they want to make all the backpacks the same, with no school supplies left over, what is the greatest number of backpacks they can fill?

backpacks

key idea

The greatest common factor is the largest whole number that is a factor of each of two or more numbers.

solution

Write the prime factorization for each number.

6	=	2 × 3

15	=	3 × 5

Next, find the common factors shared by both of the numbers.

6	=	2 × 3

15	=	3 × 5

The only common factor of 6 and 15 is 3, so the greatest common factor is 3. That means that the greatest possible number of backpacks is 3, because 6 pencils could be put into 3 backpacks with 2 pencils each and 15 notebooks could be put into 3 backpacks with 5 notebooks each.

The greatest number of backpacks they can fill is 3.

Looking for more? Try these:

Lesson: Greatest common factor

Lesson: Least common multiple

$Confetti$

Excellent!

Now entering the Challenge Zone—are you ready?

Questions
answeredQuestions

Time
elapsedTime

hr	min	sec
00	00	02

SmartScore
out of 100
IXL's SmartScore is a dynamic measure of progress towards mastery, rather than a percentage grade. It tracks your skill level as you tackle progressively more difficult questions. Consistently answer questions correctly to reach excellence (90), or conquer the Challenge Zone to achieve mastery (100)! Learn more

Teacher tools

Work it out

Not feeling ready yet? These can help:

E.2Greatest common factor

E.3Least common multiple

Lesson: Greatest common factor

Lesson: Least common multiple

Excellent! You got that right!

Jumping to level 1 of 1

Excellent!