GCF and LCM Quiz
Questions: 16 · 10 minutes
1. A teacher has 24 red counters and 36 blue counters. She wants to make the greatest possible number of identical sets with no counters left over. How many sets can she make?
12 sets
6 sets
18 sets
24 sets
2. Which statement correctly describes the relationship among the GCF, the original numbers, and the LCM?
Each original number divides the GCF, and the LCM divides each original number
The GCF divides each original number, and each original number divides the LCM
The GCF must be smaller than 1, while the LCM must exceed both numbers
The GCF and LCM must both be factors of each original number
3. A student is finding the LCM of 18 and 30 from 18 = 2 × 3² and 30 = 2 × 3 × 5. Which method gives the correct result?
Use only the shared prime factors to get 6
Multiply the original numbers to get 540
Use each prime at its greatest exponent to get 90
Use each prime at its smallest exponent to get 30
4. Which list contains every positive common factor of 18 and 24?
1, 2, and 3
1, 2, 3, 6, and 9
1, 2, 3, and 6
1, 2, 3, 4, and 6
5. A rectangular floor measures 84 cm by 126 cm in a scale model. What is the side length of the largest square tile that can cover it without cutting or gaps?
42 cm
21 cm
28 cm
14 cm
6. The prime factorizations are 72 = 2³ × 3² and 60 = 2² × 3 × 5. What is their GCF?
12
6
24
30
7. Which pair of numbers is relatively prime, meaning its GCF is 1?
12 and 18
15 and 25
14 and 21
14 and 25
8. Two positive whole numbers have a GCF of 4 and an LCM of 60. If one number is 12, what is the other number?
5
12
20
48
9. What is the greatest common factor (GCF) of two positive whole numbers?
The smallest positive number that both numbers divide evenly
The largest whole number that divides both numbers without a remainder
The product of all factors shared by the numbers
The largest multiple shared by the numbers
10. When does the LCM of two positive whole numbers equal their product?
When one number is a factor of the other
Whenever both numbers are even
When their GCF is 1
Whenever the numbers have the same number of factors
11. Two lights flash together now. One flashes every 6 minutes and the other every 8 minutes. After how many minutes will they next flash together?
24 minutes
14 minutes
36 minutes
48 minutes
12. The GCF of 24 and an unknown positive whole number is 8, while their LCM is 48. What is the unknown number?
8
12
48
16
13. A student simplifies 42/56 by dividing the numerator and denominator by their GCF. What simplified fraction results?
6/8
3/4
2/3
7/8
14. What is the least common multiple (LCM) of two positive whole numbers?
The smallest factor greater than 1 that the numbers share
The largest number that divides both numbers evenly
The result of multiplying the numbers and dividing by 2
The smallest positive number that is a multiple of both numbers
15. A craft pattern needs a strip length that can be divided into either 8 cm sections or 12 cm sections with nothing left over. What is the shortest possible strip length?
48 cm
24 cm
20 cm
16 cm
16. One bus arrives every 12 minutes and another arrives every 18 minutes. If they arrive together at 9:00 a.m., when will they next arrive together?
9:24 a.m.
10:12 a.m.
9:48 a.m.
9:36 a.m.