IXL - GCF and LCM: word problems (Algebra 1 practice)

Latrell is buying AA batteries and D batteries. The store sells AA batteries in packs of 5 and D batteries in packs of 2. If Latrell wishes to buy the same number of AA and D batteries, what is the smallest number of each battery type that he can buy?

batteries

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question

Eddie's hens lay eggs in groups of 5. Meanwhile, Jessica's hens lay eggs in groups of 2. If both chicken farmers were able to collect the same number of eggs from their chickens this week, what is the minimum number of eggs that could have been laid for each farmer?

eggs

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 5 and 2. This is the least common multiple.

5 and 2 are prime numbers. You do not need to factor them. Multiply the prime numbers:

2 × 5 = 10

The least common multiple of 5 and 2 is 10. That means that the minimum number of eggs laid by each hen this week is 10, because 2 sets of 5 eggs laid by Eddie's hen is 10 eggs in total and 5 sets of 2 eggs laid by Jessica's hen is 10 eggs in total.

The smallest number of eggs that could have been laid for each farmer is 10.

Looking for more? Try these:

Lesson: Greatest common factor

Lesson: Least common multiple

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Not feeling ready yet? These can help:

Lesson: Greatest common factor

Lesson: Least common multiple

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