Grade 6 Math Practice Test: Greatest Common Factor and Least Common Multiple
- Greatest Common Factor and Least Common Multiple
- 10 questions
- 12 minutes
This test covers finding the greatest common factor (GCF) and least common multiple (LCM), using the GCF with the distributive property, and word problems about grouping and repeating events. Tip: "split into equal groups" usually needs the GCF, "happen together again" needs the LCM.
Tap an option to mark your answer. You can change your mind, or tap the same option again to leave the question blank. The correct answers and explanations appear when you finish the test.Tap an option to answer; tap it again to leave the question blank.
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Question 1
What is the greatest common factor of 18 and 24?
Correct answer: A
Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. The greatest one they share is 6. 72 is the least common multiple.
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Question 2
What is the least common multiple of 6 and 8?
Correct answer: C
Multiples of 6: 6, 12, 18, 24 … Multiples of 8: 8, 16, 24 … The first one they share is 24. 48 is a common multiple, but not the least one.
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Question 3
Which shows 36 + 48 written as the greatest common factor times a sum?
Correct answer: D
The GCF of 36 and 48 is 12, and 36 + 48 = 12(3 + 4). The other expressions are also equal to 84, but they use a common factor that is not the greatest.
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Question 4
Hot dogs come in packs of 10, and buns come in packs of 8. Rae wants the same number of hot dogs and buns.
What is the least number of hot dogs she can buy?
Correct answer: B
The number must be a multiple of both 10 and 8, and the least common multiple is 40 (4 packs of hot dogs, 5 packs of buns). 80 also works but is not the least.
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Question 5
A teacher has 24 pencils and 36 erasers. She makes identical kits with every pencil and eraser used and nothing left over.
What is the greatest number of kits she can make?
Correct answer: C
The number of kits must divide both 24 and 36, and the greatest such number is the GCF, 12. Each kit then has 2 pencils and 3 erasers. 72 is the LCM.
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Question 6
One bus leaves a station every 12 minutes, and another leaves every 15 minutes. Both leave at 8:00 a.m.
When will they next leave at the same time?
Correct answer: A
The LCM of 12 and 15 is 60, so they leave together again after 60 minutes, at 9:00 a.m. 8:27 adds 12 and 15, and at 8:30 only the 15-minute bus leaves.
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Question 7
What is the greatest common factor of 17 and 34?
Correct answer: D
34 = 2 × 17, so 17 is a factor of both numbers, and no greater number divides 17. 1 is a common factor, but not the greatest one.
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Question 8
What is the least common multiple of 9 and 12?
Correct answer: B
Multiples of 12: 12, 24, 36 … and 36 is also a multiple of 9. 108 is 9 × 12, a common multiple but not the least. 3 is the GCF.
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Question 9
Which pair of numbers has a greatest common factor of 1?
Correct answer: C
8 = 2 × 2 × 2 and 15 = 3 × 5 share no prime factors, so their GCF is 1. 9 and 15 share 3, 10 and 25 share 5, and 14 and 21 share 7.
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Question 10
Two numbers have a greatest common factor of 4 and a least common multiple of 24. One of the numbers is 8. What is the other number?
Correct answer: B
Factors of 12 are 1, 2, 3, 4, 6, 12, so the GCF of 8 and 12 is 4, and their LCM is 24. With 16, the GCF would be 8; with 6, the GCF would be 2.
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