LCM and GCF word problems | Factors and multiples | Pre-Algebra | Khan Academy | Summary and Q&A

TL;DR

Luis's class receives 30-question exams while William's class receives 24-question exams. The minimum number of questions they can expect in a year is 120.

Key Insights

• 🏛️ Luis's class has exams with 30 questions, while William's class has exams with 24 questions.
• 🏛️ The minimum number of exam questions for both classes is 120.
• #️⃣ The difference in the number of exams is compensated by the difference in the number of questions per exam.
• 🏛️ The least common multiple (LCM) of 24 and 30 is 120, representing the minimum number of exam questions for both classes.
• ❓ Prime factorization can also be used to find the LCM.
• #️⃣ The greatest common divisor (GCD) is used to determine the greatest number of identical sets that can be created using a given number of items.
• 🌥️ The GCD of 21 and 30 is 3, indicating the largest number that can divide both quantities evenly.

Transcript

William and Luis are in different physics classes at Santa Rita. Luis's teacher always gives exams with 30 questions on them, while William's teacher gives more frequent exams with only 24 questions. Luis's teacher also assigns three projects per year. Even though the two classes have to take a different number of exams, their teachers have told th... Read More

Questions & Answers

Q: What is the minimum number of exams Luis's class can expect in a year?

Luis's class can expect a minimum of 4 exams in a year, with a total of 120 questions (30 questions per exam).

Q: How many exams does William's class need to reach the minimum number of questions?

William's class needs 5 exams to reach the minimum number of 120 questions (24 questions per exam).

Q: What do Luis and William's classes have in common regarding the number of exam questions?

Both classes can have the same total number of 120 exam questions, despite the different number of questions per exam.

Q: How did the least common multiple (LCM) help find the minimum number of exam questions?

The LCM of 24 and 30 is 120, which represents the minimum number of exam questions that satisfies both Luis and William's classes.

Summary & Key Takeaways

• Luis's class has 30-question exams and William's class has 24-question exams.

• The total number of exam questions for both classes in a year is the same.

• The minimum number of exam questions for both classes is 120.