Q. A factory produces two types of widgets. The first type is produced every 12 days and the second every 15 days. How often will both types be produced on the same day? (2023)
A.
30 days
B.
60 days
C.
45 days
D.
75 days
Solution
The LCM of 12 and 15 is 60, so both types will be produced on the same day every 60 days.
Q. A gardener has 36 red roses and 48 yellow roses. He wants to plant them in rows with the same number of each type of rose in each row. What is the maximum number of rows he can plant? (2023)
A.
6
B.
12
C.
18
D.
24
Solution
The HCF of 36 and 48 is 12, which is the maximum number of rows he can plant.
Q. A gardener has 60 red flowers and 90 yellow flowers. What is the largest number of bouquets he can make if each bouquet has the same number of red and yellow flowers? (2023)
A.
15
B.
30
C.
45
D.
60
Solution
The largest number of bouquets is the HCF of 60 and 90, which is 30.
Q. A gardener has two types of plants, one type has a height of 3 feet and the other 5 feet. What is the minimum height at which both types can be tied together? (2023)
A.
15
B.
30
C.
60
D.
45
Solution
The minimum height is the LCM of 3 and 5, which is 15 feet.
Q. A gardener has two types of plants, one type requires watering every 4 days and the other every 6 days. If both types are watered together today, in how many days will they be watered together again? (2023)
A.
12
B.
24
C.
18
D.
30
Solution
The LCM of 4 and 6 is 12. Therefore, they will be watered together again in 12 days.
Q. A group of students can complete a project in 12 days. If 4 more students join, the project can be completed in 8 days. How many students were initially in the group? (2023)
A.
6
B.
8
C.
10
D.
12
Solution
Let the initial number of students be x. The work done is constant, so x * 12 = (x + 4) * 8. Solving gives x = 8.
Q. A group of students can complete a project in 12 days. If 4 more students join, they can complete it in 8 days. How many students were initially in the group?
A.
6
B.
8
C.
10
D.
12
Solution
Let the initial number of students be x. The work done is inversely proportional to the number of days. Setting up the equation gives x = 10.
Q. A teacher has 48 pencils and 60 erasers. She wants to distribute them equally among students. What is the maximum number of students she can distribute to? (2023)
A.
12
B.
6
C.
8
D.
10
Solution
The HCF of 48 and 60 is 12, which is the maximum number of students she can distribute to equally.
Q. If the HCF of two numbers is 5 and their LCM is 100, what is the sum of the two numbers? (2023)
A.
30
B.
25
C.
50
D.
45
Solution
Let the two numbers be 5x and 5y. Then, HCF(5x, 5y) = 5 and LCM(5x, 5y) = 100. This gives xy = 20. The pairs (x, y) that satisfy this are (4, 5) or (5, 4), leading to the sum 5(4 + 5) = 45.
Understanding HCF (Highest Common Factor) and LCM (Lowest Common Multiple) is crucial for students preparing for school and competitive exams. These concepts not only form the foundation of number theory but also frequently appear in various exam formats. Practicing HCF & LCM MCQs and objective questions helps students enhance their problem-solving skills and boosts their confidence, ensuring they are well-prepared for important questions in their exams.
What You Will Practise Here
Definition and significance of HCF and LCM
Methods to calculate HCF and LCM, including prime factorization and listing multiples
Applications of HCF and LCM in real-life scenarios
Formulas related to HCF and LCM
Common problems and practice questions on HCF and LCM
Visual aids and diagrams to understand concepts better
Tips and tricks for quick calculations
Exam Relevance
The concepts of HCF and LCM are integral to the mathematics syllabus across various educational boards in India, including CBSE and State Boards. These topics are frequently tested in school exams and competitive exams like NEET and JEE. Students can expect questions that require them to find the HCF or LCM of given numbers, often in multiple-choice formats. Understanding the common question patterns can significantly enhance exam performance.
Common Mistakes Students Make
Confusing HCF with LCM and vice versa
Incorrect application of formulas, especially in word problems
Overlooking the importance of prime factorization in calculations
Rushing through calculations, leading to simple arithmetic errors
Failing to check if the answer is reasonable based on the problem context
FAQs
Question: What is the difference between HCF and LCM? Answer: HCF is the largest number that divides two or more numbers, while LCM is the smallest number that is a multiple of two or more numbers.
Question: How can I quickly find the HCF of two numbers? Answer: You can find the HCF using the prime factorization method or by using the Euclidean algorithm for faster calculations.
Question: Are there any shortcuts for calculating LCM? Answer: Yes, one effective shortcut is to use the formula: LCM(a, b) = (a * b) / HCF(a, b).
Now that you have a clear understanding of HCF and LCM, it's time to put your knowledge to the test! Dive into our practice MCQs and challenge yourself to solve important HCF & LCM questions for exams. Your preparation starts here!
Soulshift Feedback×
On a scale of 0–10, how likely are you to recommend
The Soulshift Academy?
