GCD and LCM Fundamentals Basics

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Cierra Henderson, MBA |
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Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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| Attempts: 24 | Questions: 20 | Updated: Jan 20, 2026
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1) The GCD of 18 and 24 is:

Explanation

18 = 2 × 3² and 24 = 2³ × 3. The common primes are one 2 and one 3 → 2 × 3 = 6.

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About This Quiz
GCD and LCM Fundamentals Basics - Quiz

Want to strengthen your skills with factors and multiples? In this quiz, you’ll practice finding the Greatest Common Divisor (GCD) and Least Common Multiple (LCM) of different numbers. You’ll explore prime factorizations, test for coprime pairs, and even solve real-world cycle problems like bells ringing or trains arriving. Take this... see morequiz to build a solid foundation in GCD and LCM!
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2) Which is the prime factorization of 60?

Explanation

Break 60 down: 60 = 2 × 2 × 3 × 5. That’s 2 × 2 × 3 × 5.

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3) The GCD of 45 and 60 is:

Explanation

45 = 3² × 5 and 60 = 2² × 3 × 5 → common = 3 × 5 = 15.

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4) LCM(12, 15) = ?

Explanation

12 = 2² × 3 and 15 = 3 × 5 → 2² × 3 × 5 = 60.

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5) LCM(9, 12) is:

Explanation

9 = 3²; 12 = 2² × 3 → highest powers 2² × 3² = 36.

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6) A teacher arranges chairs in rows of 12 or 18. Least number of chairs possible?

Explanation

We need a size both 12 and 18 fit into → LCM(12, 18) = 36 chairs.

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7) Which of these equals LCM(20, 30)?

Explanation

20 = 2² × 5; 30 = 2 × 3 × 5 → 2² × 3 × 5 = 60.

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8) A bell rings every 15 minutes, another every 20 minutes. After how many minutes together?

Explanation

Ring together at LCM(15, 20) = 60 minutes.

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9) GCD(28, 49) = ?

Explanation

28 = 2² × 7; 49 = 7² → common = 7.

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10) LCM(14, 21) = ?

Explanation

14 = 2 × 7; 21 = 3 × 7 → 2 × 3 × 7 = 42.

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11) GCD(120, 150) = ?

Explanation

120 = 2³ × 3 × 5; 150 = 2 × 3 × 5² → common = 2 × 3 × 5 = 30.

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12) Two trains whistle every 12 and 18 minutes. After how many minutes together?

Explanation

Together at LCM(12, 18) = 36 minutes.

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13) GCD(63, 81) = ?

Explanation

63 = 3² × 7; 81 = 3⁴ → common = 3² = 9.

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14) GCD(144, 192) = ?

Explanation

144 = 2⁴ × 3²; 192 = 2⁶ × 3 → common = 2⁴ × 3 = 48.

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15) The LCM of 6 and 8 is:

Explanation

6 = 2 × 3 and 8 = 2³. Take the highest powers: 2³ × 3 = 24.

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16) GCD(72, 90) = ?

Explanation

72 = 2³ × 3²; 90 = 2 × 3² × 5 → common = 2 × 3² = 18.

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17) If GCD(a, b) = 1, then a and b are:

Explanation

That means they share no prime factors → relatively prime.

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18) LCM(16, 24) = ?

Explanation

16 = 2⁴; 24 = 2³ × 3 → 2⁴ × 3 = 48.

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19) GCD(36, 84) is:

Explanation

36 = 2² × 3²; 84 = 2² × 3 × 7 → common = 2² × 3 = 12.

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20) Which pair is coprime?

Explanation

(8, 9) share no common prime factors (2’s vs 3²), so they’re coprime.

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Cierra Henderson |MBA |
K-12 Expert
Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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The GCD of 18 and 24 is:
Which is the prime factorization of 60?
The GCD of 45 and 60 is:
LCM(12, 15) = ?
LCM(9, 12) is:
A teacher arranges chairs in rows of 12 or 18. Least number of chairs...
Which of these equals LCM(20, 30)?
A bell rings every 15 minutes, another every 20 minutes. After how...
GCD(28, 49) = ?
LCM(14, 21) = ?
GCD(120, 150) = ?
Two trains whistle every 12 and 18 minutes. After how many minutes...
GCD(63, 81) = ?
GCD(144, 192) = ?
The LCM of 6 and 8 is:
GCD(72, 90) = ?
If GCD(a, b) = 1, then a and b are:
LCM(16, 24) = ?
GCD(36, 84) is:
Which pair is coprime?
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