IXL | GCF and LCM: word problems

At a school event, adults are seated in groups of exactly 11 and children are seated in groups of exactly 5. If there are the same number of adults as children, what is the minimum number of adults attending?

adults

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question

At a party, the cheese pizza is cut into 15 slices and the veggie pizza is cut into 6 slices. If the host wants to serve identical platters that contain the same combination of cheese and veggie slices, with no slices left over, what is the greatest number of platters the host can prepare?

platters

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.

15	=	3 × 5

6	=	2 × 3

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

15	=	3 × 5

6	=	2 × 3

The only common factor of 15 and 6 is 3, so the greatest common factor is 3. That means that the greatest possible number of platters is 3, because 15 slices of cheese pizza could be put onto 3 platters with 5 slices of cheese pizza each and 6 slices of veggie pizza could be put onto 3 platters with 2 slices of veggie pizza each.

The greatest number of platters the host can prepare is 3.

Looking for more? Try these:

Lesson: Greatest common factor

Lesson: Least common multiple

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E.2Greatest common factor

E.3Least common multiple

Lesson: Greatest common factor

Lesson: Least common multiple

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