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Quizzes > High School Quizzes > Mathematics

Common Multiples Practice Quiz

Interactive worksheet challenges to boost math confidence

Difficulty: Moderate
Grade: Grade 5
Study OutcomesCheat Sheet
Colorful paper art promoting The Common Multiples Challenge math trivia for middle school students.

What is a common multiple?
A number that divides two or more numbers exactly
A number that is always even
A number that is a multiple of two or more numbers
A number that is added to another number
A common multiple is defined as a number that is a multiple of two or more numbers. This means that it can be obtained by multiplying each of the given numbers by some integer.
Find a common multiple of 4 and 6 that is less than 30.
20
12
16
18
12 is a common multiple of 4 and 6 because 4 - 3 = 12 and 6 - 2 = 12. The other numbers either do not divide evenly by both 4 and 6 or are not within the specified range.
Which of the following is a method to find common multiples?
Multiply the numbers together
List the multiples of each number and identify those that appear in both lists
Find the average of the numbers
Subtract one number from the other
Listing the multiples of each number and then finding the common ones is a straightforward method to identify common multiples. Other methods listed do not reliably find common multiples.
What is the Least Common Multiple (LCM) of 3 and 5?
15
10
9
30
15 is the smallest number that both 3 and 5 divide evenly into, making it the least common multiple. The other options are either too large or not divisible by one of the numbers.
Which of the numbers below is a common multiple of 2, 3, and 4?
18
8
10
12
12 is divisible by 2, 3, and 4, making it a common multiple of all three numbers. The other options fail to be divisible by at least one of the numbers.
What is the LCM of 6 and 8 using their prime factors?
18
24
48
16
By prime factorization, 6 = 2 - 3 and 8 = 2³. Taking the highest power of each prime, the LCM is 2³ - 3 = 24. The other choices do not incorporate the prime factors correctly.
Find the LCM of 14 and 20.
70
140
280
100
14 factors into 2 - 7 and 20 factors into 2² - 5. The LCM is calculated by taking the highest powers of the primes: 2², 7, and 5, which multiply to 140. The other options either omit necessary factors or are not the least common multiple.
Identify the first common multiple of 4, 6, and 9.
48
36
18
24
Multiples of 4, 6, and 9 overlap first at 36, making it the smallest common multiple. The other numbers do not satisfy the conditions for all three.
Which technique is most effective in finding the LCM of two large numbers?
Listing all multiples
Adding the two numbers
Subtracting the smaller from the larger repeatedly
Using prime factorization to combine the highest powers of all factors
Prime factorization is efficient and accurate for finding the LCM of large numbers by identifying all necessary factors. The other techniques are either too time”consuming or not logically connected to finding common multiples.
Calculate the LCM of 9 and 12.
24
18
36
30
The prime factors of 9 are 3² and of 12 are 2² - 3. Taking the highest powers for each prime gives 2² - 3² = 36 as the LCM. The other options do not incorporate all necessary factors.
Given that LCM(12, x) is 60, which of the following cannot be the value of x?
10
25
20
15
For LCM(12, x) to equal 60, x must complement the prime factors of 12 (2² - 3) by contributing a factor of 5 without introducing extra primes. The number 25 (5²) increases the power of 5 beyond what is needed, making the LCM greater than 60. Therefore, 25 is not a possible value for x.
Which of the following statements about common multiples is true?
Every common multiple of two numbers is a divisor of their LCM
Common multiples are always smaller than the original numbers
Every multiple of a number is a common multiple of any other number
Every common multiple of two numbers is a multiple of their LCM
The least common multiple (LCM) is a factor of every common multiple of two numbers. This makes the statement that every common multiple is a multiple of the LCM true. The other assertions are incorrect and do not accurately describe the relationship.
If the LCM of two numbers equals their product, what can you conclude about the two numbers?
They are both prime
They share all common factors
They are relatively prime
They are consecutive numbers
When the LCM of two numbers equals their product, it indicates that the numbers have no common factors other than 1, meaning they are relatively prime. The other choices either oversimplify or are unrelated to this key property.
Find the LCM of 11 and 13.
121
24
169
143
Since 11 and 13 are both prime numbers, their LCM is simply their product, which is 143. The other answers do not correctly represent this multiplication of two distinct primes.
What is the first common multiple of 5, 10, and 20?
40
30
10
20
20 is the smallest number that is a multiple of 5, 10, and 20. It meets the divisibility requirement for all three numbers, whereas the other options either fall short or exceed the conditions of being the first common multiple.
Determine the LCM of 16, 20, and 24 using prime factorization.
120
240
480
60
First, factor each number: 16 = 2❴, 20 = 2² - 5, and 24 = 2³ - 3. The LCM is found by taking the highest power of each prime: 2❴, 3, and 5, resulting in 16 - 3 - 5 = 240. The other options either miss a prime factor or do not use the highest exponents.
If the LCM of two numbers is 84 and one of the numbers is 12, what is the greatest possible value for the other number that still maintains the LCM of 84?
84
28
42
56
The number 12 factors as 2² - 3 and 84 factors as 2² - 3 - 7. To keep the LCM exactly 84, the other number must introduce the factor 7 without adding extra powers of 2 or 3. Thus, the maximum value it can be is 84 itself.
Which of the following represents the kth common multiple of two numbers, given that their LCM is L?
L raised to the power of k
k - L
k plus the product of the two numbers
L + k
Since all common multiples of two numbers are multiples of their LCM, the kth common multiple is simply k multiplied by the LCM (L). The other options do not correctly represent the sequence of common multiples.
Find the LCM of 6, 8, and 15.
90
240
120
60
Break down the numbers into primes: 6 = 2 - 3, 8 = 2³, and 15 = 3 - 5. Taking the highest powers gives 2³, 3, and 5, so the LCM is 8 - 3 - 5 = 120. The other choices do not incorporate the required prime factors appropriately.
For numbers 9, 12, and 21, determine the LCM by identifying their prime factors.
378
126
252
84
Decompose the numbers: 9 = 3², 12 = 2² - 3, and 21 = 3 - 7. The LCM is obtained by taking 2² from 12, 3² from 9, and 7 from 21, which results in 4 - 9 - 7 = 252. The other options either miss a prime factor or do not use the correct exponents.
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Study Outcomes

  1. Understand the definition and concept of common multiples.
  2. Identify common multiples in a given set of numbers.
  3. Calculate the least common multiple for various number pairs.
  4. Apply problem-solving strategies to determine common multiples.
  5. Analyze errors in solution approaches to improve accuracy.

Common Multiples Worksheet Cheat Sheet

  1. Understanding Multiples - A multiple of a number is what you get when you multiply that number by an integer. Think of it as hopping along the number line in equal jumps like 3, 6, 9, and 12. Multiples pop up everywhere, from rhythm beats to calendar cycles. Cuemath: Common Multiples
  2. Identifying Common Multiples - Common multiples appear when two or more numbers share the same multiples. For instance, both 3 and 4 list 12 in their sequences of jumps. Spotting these helps solve puzzles and sync events that repeat over time. Maths Teacher AU: Common Multiples
  3. Least Common Multiple (LCM) - The LCM is the smallest positive number that appears in the multiple lists of two or more numbers. It's like finding the first party where all your number friends show up together. For example, LCM of 4 and 5 is 20. Online Math Learning: LCM Basics
  4. Finding LCM by Listing Multiples - Listing multiples is the most visual method to find the LCM: write out the sequences and spot the first overlap. For 3 and 4, list [3, 6, 9, 12] and [4, 8, 12] to see 12 as the winner. It's a hands-on way to understand patterns. Cuemath: Listing Method
  5. Prime Factorization Method - Break each number into its prime factors (like 2, 3, 5) and take the highest power of each prime to build your LCM. It's a neat toolbox approach that scales well for bigger numbers. This method also shows why primes are so important. Cuemath: Prime Factorization
  6. Division Method for LCM - Divide numbers by common primes step by step until only 1s remain, then multiply all the divisors to get the LCM. It's like simplifying in reverse with a collaborative twist. This keeps your workspace tidy and organized. Cuemath: Division Method
  7. LCM of Co-Prime Numbers - When two numbers share no factors other than 1, they're co-prime. Their LCM is simply their product, making things extra easy! For example, LCM(3, 5) = 3 × 5 = 15 without any extra steps. SplashLearn: Co-Prime LCM
  8. LCM in Word Problems - Word problems often hide LCM puzzles, like figuring out when two blinking lights will flash in unison again. Translating text into numbers reveals repeating cycles to sync up events. It's a real-world detective game for math enthusiasts. Online Math Learning: Word Problems
  9. Practice with Real-Life Scenarios - Apply LCM to daily challenges like planning schedules, lining up class periods, or matching exercise intervals. Turning abstract numbers into real tasks cements your understanding. Grab a calendar and some sticky notes to experiment! Online Math Learning: Real-Life Practice
  10. Utilize Online Resources - Interactive lessons, videos, and quizzes make mastering multiples and LCM a breeze. Dive into games to test your speed or watch short tutorials for clarifications. Learning becomes fun when you level up like in video games! National Academy: Interactive Lessons
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