HCF(GCD,GCF) and LCM

Last Updated : 4 January 2023, Thursday

Table of Topics
Introduction
HCF
LCM
Quiz

Introduction

HCF (Highest Common Factor) and LCM (Lowest Common Multiple) are fundamental concepts in mathematics that play a crucial role in various mathematical operations and problem-solving. They are particularly important in number theory, algebra, and many real-world applications. In this article, we will delve into these two concepts, exploring their definitions and their calculation methods.

HCF

HCF, also known as GCD (Greatest Common Divisor), is the largest positive integer that divides two or more given numbers without leaving a remainder. It represents the highest factor that is common to all the numbers in question. The HCF is an essential concept in simplifying fractions and solving problems related to ratios, proportions, and divisibility.

Prime Factorisation Method to find HCF of 2 or more numbers

  • Express each number as a product of its prime factors.
  • Identify the common prime factors and find the smallest exponent for each common factor.
  • Multiply the common prime factors with the smallest exponent to obtain the HCF.

Division method to find HCF of 2 numbers:

  • Divide the larger number by the smaller one.
  • Replace the larger number with the smaller one and the smaller number with the remainder obtained.
  • Repeat this process until the remainder becomes zero.
  • The divisor at this point is the HCF of the two numbers.

Division method to find HCF of more than 2 numbers:

  • Start by finding the HCF of the first two numbers using the division method, as explained earlier.
  • Once you have the HCF of the first two numbers, you can then find the HCF of this result and the next number.
  • Repeat this process for each additional number, using the HCF obtained in the previous step along with the next number, until you have gone through all the numbers.
  • The final result is the HCF of all the numbers.

LCM

  • LCM, also known as the least common multiple, is the smallest positive integer that is a multiple of two or more given numbers. It represents the smallest number at which the given numbers have a common multiple. LCM is frequently used in applications such as finding a common denominator for fractions and solving problems related to time, distance, and periodic events.
  • To calculate the LCM of two or more numbers, you can use various methods, including the prime factorization method, listing multiples, and the division method. Here, we will discuss the prime factorization method:
  • A) Express each number as a product of its prime factors.

B) Identify all unique prime factors among these numbers.

C) Calculate the LCM by multiplying these unique prime factors with their highest exponents

Quiz

HCF and LCM

Questions 1-10 have single answer correct

Questions 11-20 have 1 or more than 1 correct answers

1 / 20

If the HCF (Highest Common Factor) of 210 and 55 is expressible in the form of 210x + 55y where x, y are integers, then what is one possible value of x?

2 / 20

What is the HCF of 36 and 48?

3 / 20

Find the LCM of 15 and 20.

4 / 20

Which of the following is true for any two numbers, a and b?

5 / 20

The LCM of two numbers is 840 and their HCF is 7. If one of the numbers is 105, what is the other number?

6 / 20

What is the smallest number which when divided by 20 and 28 leaves a remainder of 5 in each case?

7 / 20

Which of the following is NOT a prime factor of the LCM of 18, 24, and 36?

8 / 20

If the HCF of a and 18 is 6 and their LCM is 36, what is one possible value of a?

9 / 20

Two numbers are in the ratio 3:4. If their LCM (Least Common Multiple) is 180, what is the sum of these two numbers?

10 / 20

Find the HCF of 56, 112, and 168.

11 / 20

What is the HCF of 24 and 36?

12 / 20

Which of the following pairs have LCM as 20?

13 / 20

For two prime numbers p and q, where p q, what is the HCF?

14 / 20

What is the LCM of 12, 15, and 20?

15 / 20

Select the pairs that have an HCF of 1.

16 / 20

Which numbers have 36 as their LCM?

17 / 20

If the HCF of two numbers is 11 and their LCM is 770, what is one possible pair of these two numbers?

18 / 20

Which of the following is/are true about HCF and LCM of two numbers a and b? (a>0,b>0)

19 / 20

Which of the following statements are true about HCF and LCM?

20 / 20

What is the LCM of two prime numbers 13 and 17?

Your score is

The average score is 0%

0%