Math Quiz: HCF and LCM Concepts

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Questions and Answers

What is the highest common factor (HCF) of the numbers 24, 36, and 60?

The HCF is 12.

How do you find the least common multiple (LCM) of 4, 5, and 6?

The LCM is 60.

Explain the relationship between factors and multiples.

Factors are numbers that divide another number without a remainder, while multiples are the products obtained when a number is multiplied by integers.

What real-life situation can be modeled using the concept of LCM?

LCM can be used to determine when two events, like the recycling truck and garbage truck, will arrive on the same day again. Signup and view all the answers

Calculate the HCF of 30, 45, and 75 using prime factorization.

The HCF is 15. Signup and view all the answers

What role does the concept of multiples play in determining the LCM?

The LCM is derived from the multiples of the given numbers, specifically the smallest one that appears in all sets. Signup and view all the answers

In what way do HCF and LCM help in simplifying fractions?

They help in finding the simplest form by dividing both the numerator and denominator by their HCF. Signup and view all the answers

Provide a practical example where factors can be useful in real life.

Determining how to evenly distribute 28 apples among 4 friends can be done using factors. Signup and view all the answers

What is the relationship between factors and multiples?

Factors are the numbers that divide another number evenly, whereas multiples are obtained by multiplying a number by integers. Signup and view all the answers

In the context of the multiplication table, how would you define the multiples of 2?

The multiples of 2 are obtained by multiplying 2 with all integers, resulting in numbers like 2, 4, 6, 8, ..., up to 30. Signup and view all the answers

How do you determine the HCF of two numbers using their factors?

The HCF is found by identifying the highest common factor shared between the factors of the two numbers. Signup and view all the answers

Using the numbers 12 and 18, what is their LCM?

The LCM of 12 and 18 is 36. Signup and view all the answers

If Rajdeep's father sold 125 guavas for Rs 2 each, how much money did he make?

He made Rs 250 by selling 125 guavas at Rs 2 each. Signup and view all the answers

Explain why the multiples of 3 are considered infinite.

The multiples of 3 are infinite because you can keep multiplying 3 by larger integers without limit. Signup and view all the answers

Define how HCF can be useful in simplifying fractions.

HCF helps in simplifying fractions by dividing both the numerator and the denominator by their highest common factor. Signup and view all the answers

In the context of real-life situations, how can knowing LCM be beneficial?

Knowing the LCM allows individuals to find a common period for events that repeat, such as scheduling activities or coordinating timings. Signup and view all the answers

What is the highest common factor (HCF) of 36 and 24?

The HCF of 36 and 24 is 12. Signup and view all the answers

Calculate the least common multiple (LCM) of 4 and 5.

The LCM of 4 and 5 is 20. Signup and view all the answers

If you have 12 apples and want to distribute them among 4 friends equally, how many apples will each friend receive?

Each friend will receive 3 apples. Signup and view all the answers

What are the factors of 30?

The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30. Signup and view all the answers

If a rectangle has a length of 10 meters and width of 5 meters, what is the area?

The area of the rectangle is 50 square meters. Signup and view all the answers

Find the GCF of 18 and 27 using prime factorization.

The GCF of 18 and 27 is 9. Signup and view all the answers

What is the significance of finding the LCM in scheduling events?

The LCM helps to determine when events will coincide or repeat. Signup and view all the answers

How can you find the multiples of 7 up to 70?

The multiples of 7 up to 70 are 7, 14, 21, 28, 35, 42, 49, 56, 63, 70. Signup and view all the answers

Study Notes

Book Title and Class

GANITPRABHA
Class VI

Publication Information

Eighth Edition : December, 2020
West Bengal Board of Secondary Education
Published by Smt. Paromita Roy
Secretary-in-charge
West Bengal Board of Secondary Education
77/2, Park Street, Kolkata - 700016
Printed at West Bengal Text Book Corporation Limited (Government of West Bengal Enterprise)
Kolkata-700 056

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Description

Test your knowledge on the highest common factor (HCF) and least common multiple (LCM). This quiz explores their definitions, relationships, calculations, and real-life applications. Enhance your understanding of these fundamental mathematical concepts.