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Quizzes > High School Quizzes > Mathematics

Lowest Common Multiple Practice Quiz

Sharpen your skills with engaging word problems

Difficulty: Moderate
Grade: Grade 6
Study OutcomesCheat Sheet
Colorful paper art promoting LCM Word Quest, a math trivia quiz for middle school students.

Samantha has packs of pencils containing 4 pencils each and erasers that come in packs of 6. What is the smallest total number of items she can have so that both pencils and erasers can be evenly arranged?
12
18
24
30
The least common multiple (LCM) of 4 and 6 is 12 because 12 is the smallest number that is a multiple of both. This means buying packs to reach 12 items will allow an even arrangement.
Jason practices jump rope using cycles of 3 and 5. What is the least number of cycles before the patterns align?
15
10
20
30
Since 3 and 5 are relatively prime, their LCM is simply their product, 15. This is the first cycle at which both events occur together.
A teacher wishes to arrange students in teams of 2 or 7 with no one left over. What is the smallest number of students that works for both team sizes?
14
7
21
12
The LCM of 2 and 7 is 14 because 14 is the smallest number that is a multiple of both 2 and 7. This number works perfectly for arranging teams evenly.
A school event displays flags in rows of 8 and groups of 6. What is the minimum number of flags required to form complete rows or groups?
24
18
32
28
The flags need to be arranged in groups where the total is a common multiple of both 8 and 6. The LCM of 8 and 6 is 24, making it the correct number.
A stamp collector uses albums that hold 5 stamps per page and 10 stamps per page. What is the smallest number of stamps that can completely fill a page in either album?
10
5
15
20
The LCM of 5 and 10 is 10 since 10 is the smallest common multiple of both numbers. This ensures that one album page or two pages (if using the 5-stamp album) will be evenly filled.
Two buses arrive at intervals of 12 minutes and 18 minutes respectively. After how many minutes will both buses arrive at the same time?
36
24
30
48
The LCM of 12 and 18 is calculated by taking the highest power of prime factors, which yields 36. Therefore, the buses will coincide every 36 minutes.
A baker makes cookies in batches: one type comes in packs of 8 and another in packs of 12. What is the smallest number of cookies that can be evenly divided into both batch sizes?
24
16
20
30
To determine the number that works for both pack sizes, find the LCM of 8 and 12. The calculation shows 24 is the smallest number that both 8 and 12 divide evenly into.
Two runners are practicing laps. Runner A completes a lap every 5 minutes and Runner B every 7 minutes. When will both runners finish a lap together?
35
30
25
42
Since 5 and 7 are both prime relative to each other, the LCM is 35, which is their product. This is the correct time interval for both runners to finish together.
At a party, a music playlist repeats every 15 minutes while a dance routine repeats every 20 minutes. After how many minutes will these events occur simultaneously?
60
30
40
45
The LCM of 15 and 20 is 60, found by using their prime factorization. This means both events will coincide every 60 minutes.
A gardener plants flowers in rows that repeat every 6 rows and shrubs in rows that repeat every 9 rows. What is the minimum number of rows at which both patterns align?
18
12
15
21
The least common multiple of 6 and 9 is 18. This ensures that every 18 rows, the planting pattern for both flowers and shrubs aligns perfectly.
At a festive event, one banner's pattern repeats every 10 meters and another every 15 meters along a wall. What is the smallest distance at which both patterns coincide?
30
15
25
45
Calculating the LCM of 10 and 15 gives 30 meters. This is the minimum distance at which the two banner patterns will match up along the wall.
Shawn claps in two different rhythms: one every 4 beats and another every 6 beats. After how many beats will both rhythms coincide?
12
8
10
16
The LCM of 4 and 6 is 12, meaning the two clapping patterns will synchronize every 12 beats. This answer is derived by combining the highest powers of the prime factors.
Along a street, recycling bins are placed at intervals of 8 meters and 12 meters. What is the smallest distance at which a bin appears in both intervals?
24
16
20
32
By finding the least common multiple of 8 and 12, we determine that 24 meters is the smallest distance where bins from both intervals coincide. This uses the prime factorization method.
A clock factory packs clocks in boxes of 6 and sets of 9. What is the least number of clocks that can be evenly distributed into both types of packaging?
18
12
15
20
The LCM of 6 and 9 is 18, meaning that 18 clocks can be evenly divided into packages of both sizes. This ensures there is no remainder in the distribution process.
At a school fair, one display resets every 10 minutes while another resets every 14 minutes. When will both displays reset at the same time?
70
56
84
98
The LCM of 10 and 14 is 70, found by multiplying the highest powers of each prime factor. This means both displays will coincide in their reset every 70 minutes.
At a sports event, three teams have practice sessions that repeat every 3, 4, and 6 days respectively. What is the least number of days until all teams practice on the same day?
12
18
24
36
The LCM of 3, 4, and 6 is 12 because it takes the highest powers of each prime factor. Therefore, all teams will meet every 12 days for a joint practice.
A factory has three assembly lines that produce widgets every 5, 7, and 11 minutes. If they start simultaneously, after how many minutes will all three lines produce a widget at the same time?
385
350
420
330
Since 5, 7, and 11 are all prime numbers, the LCM is simply their product, which is 385 minutes. This is the first time all three assembly lines synch up.
During a science experiment, three cycles occur every 8, 9, and 15 minutes. What is the smallest duration after which all three cycles align at the starting point?
360
270
300
450
The LCM of 8, 9, and 15 is calculated by using the highest powers of the prime factors (2³, 3², and 5) which results in 360 minutes. This is the duration at which all cycles restart together.
In an art class, red beads come in packs of 12, blue beads in packs of 15, and green beads in packs of 20. What is the least number of beads needed so that each pack size divides evenly into that number?
60
120
30
90
Finding the LCM of 12, 15, and 20 involves using the highest powers of the prime factors, which gives 60 as the smallest number divisible by all three. This ensures an even division among the bead packs.
At a community center, dance, music, and art classes start at intervals of 6, 8, and 10 minutes respectively. After how many minutes will all classes start simultaneously again?
120
60
80
100
The LCM of 6, 8, and 10 is determined by taking the highest powers of their prime factors, resulting in 120 minutes. Thus, all three classes will start at the same time every 120 minutes.
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Study Outcomes

  1. Analyze word problems to identify the need for calculating the least common multiple.
  2. Apply LCM calculation methods to solve multi-step scenarios.
  3. Synthesize numerical data from problems to determine common multiples efficiently.
  4. Evaluate solution strategies to select the most effective approach for LCM problems.
  5. Reflect on performance to enhance problem-solving techniques in applied math tasks.

Lowest Common Multiple Word Problems Cheat Sheet

  1. Grasp LCM Fundamentals - The Least Common Multiple (LCM) is the smallest number both given numbers divide into evenly. Spotting the LCM helps you sync cycles, schedule events, and tackle fraction puzzles without stress. Correctly formatted link
    2. MathCounts.org
  2. Use Prime Factorization - Break each number into prime factors, then take the highest power of each prime to build the LCM. For example, 15 = 3×5 and 20 = 2²×5, so the LCM is 2²×3×5 = 60. Correctly formatted link
    3. ByteLearn.com
  3. Tackle Word Problems - Apply LCM to find when repeating events align. If one alarm rings every 6 days and another every 4 days, they'll coincide every 12 days - perfect for planning! Correctly formatted link
    4. CCSSMathAnswers.com
  4. LCM vs. GCF - Know the difference: LCM is the smallest common multiple, while GCF is the largest common factor. Mixing them up can lead to messy answers - so keep them straight! Correctly formatted link
    5. Twinkl.com
  5. Real‑Life Scheduling - Sync buses, trains, or daily routines by finding when cycles overlap. If one bus comes every 15 minutes and another every 20, they'll meet every 60 minutes. Correctly formatted link
    6. Basic‑Mathematics.com
  6. Check with GCF - Use the neat fact: for any two numbers, LCM × GCF = product of the numbers. It's a quick way to verify you didn't slip up on your calculation. Correctly formatted link
    7. MathCabin.com
  7. Mix Up Your Practice - The more LCM problems you try, the sharper your number sense becomes. Jump between simple sets and tricky word problems to stay on your toes. Correctly formatted link
    8. HackMath.net
  8. Prime Number Shortcut - For two primes, the LCM is just their product since they share no factors other than 1. So LCM(7,11) is 7×11=77 - easy! Correctly formatted link
    9. ByteLearn.com
  9. Find Common Denominators - Use LCM to add or subtract fractions with different denominators. Converting to a common denominator makes fraction arithmetic a breeze. Correctly formatted link
    10. CCSSMathAnswers.com
  10. Build Quick‑Scan Skills - Memorize multiplication tables and spot factor patterns to zero in on LCM fast. These habits save time and keep your brain fitness in top shape. Correctly formatted link
    11. MathCounts.org
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