IXL | GCF and LCM: word problems

Russell is packing equal numbers of apple slices and grapes for snacks. Russell bags the apple slices in groups of 6 and the grapes in groups of 10. What is the smallest number of grapes that he can pack?

grapes

ref_doc_title.

Learn with an example

question

Franklin and his friends made dinner reservations at two local restaurants on two different days. While the first restaurant sat all the friends in groups of 3, the second restaurant sat all the friends in groups of 9. What is the smallest number of people that could be in the group?

people

key idea

The least common multiple is the smallest whole number that is a multiple of each of two or more numbers.

solution

You need to find the smallest number that is a multiple of both 3 and 9. This is the least common multiple.

Write the prime factorization for each number. 3 is a prime number. You do not need to factor 3.

3
9 = 3 × 3

Repeat each prime factor the most number of times it appears in any of the prime factorizations above.

The most the factor 3 appears is twice.

So, multiply:

3 × 3 = 9

The least common multiple of 3 and 9 is 9. That means that the smallest possible number of people in the group is 9, because 3 tables of 3 friends is 9 people in total and 1 table of 9 friends is 9 people in total.

The smallest number of people that could be in the group is 9.

Looking for more? Try these:

Lesson: Greatest common factor

Lesson: Least common multiple

$Confetti$

Excellent!

Now entering the Challenge Zone—are you ready?

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!