IXL | GCF and LCM: word problems

William watered all the flowers at a business park. While watering, he noticed the daisies had been planted in groups of 6 and the lilies had been planted in groups of 9. If William watered the same number of each flower, what is the minimum number of each that he must have watered?

flowers

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question

Gwen has two pieces of twine, one 9 feet long and the other 15 feet long. If she wants to cut them up to produce many pieces of twine that are all of the same length, with no twine left over, what is the greatest length, in feet, that she can make them?

feet

key idea

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

solution

List the factors of each number. Find the largest number that appears in both lists.

Factors of 9:	9, 3, 1
Factors of 15:	15, 5, 3, 1

The greatest common factor of 9 and 15 is 3. That means that the longest possible piece of cut twine is 3 feet long, because the 9-foot piece of twine could be cut into 3 pieces that are 3 feet long and the 15-foot piece of twine could be cut into 5 pieces that are 3 feet long.

The greatest length the twine can be cut to is 3 feet.

Looking for more? Try these:

Lesson: Greatest common factor

Lesson: Least common multiple

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F.6Greatest common factor

F.8Least common multiple

Lesson: Greatest common factor

Lesson: Least common multiple

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