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When it comes to government examinations such as the SSC CGL exams, there are various mathematics and related questions that can be confusing to solve. One such question type found throughout MBA, banking, government, and other tests are LCM and HCF problems.
These questions require you to find the LCM and HCF of a given set of numbers using various formulas and methods. Unless you have a prior understanding of these terms and how these values are derived, they can cause some trouble. This article will learn about these questions and some simple methods to solve LCM and HCF problems.
What are the LCM and HCF?
LCM
This value is the Least Common Multiple and is the smallest number that is a multiple of a given set of numbers. So, it is essentially the first number that arises in the list of common multiples of a pair or group of numbers. For example, the LCM of 2 and 3 would be six as it is the first/smallest number in both number multiplication tables.
HCF
This term refers to the Highest Common Factor, the largest number that a set of natural numbers can be divided by. For example, if you were asked to find the HCF of 10, 20, and 1100. The answer would be ten, as it is the greatest number that can be used to divide the provided numbers without reaching an integer answer.
Simple Methods To Solve LCM and HCF Problems
To help you calculate the LCM and HCF, here are some simple methods to solve LCM and HCF problems:
HCF by Prime Factorization Method
Using this method to find the highest common factor, you will first need to perform prime factorisation on the given numbers. Once this is done and you have the prime factors, identify the common factors with the lowest power and multiply them with each other. The product of this calculation will be the highest common factor of the set of numbers.
For example, find the HCF of 10 and 24 with the prime factorisation method.
You would first write the numbers as their prime factors to solve this.
10 = 2 x 5
24 = 2 x 2 x 2 x 3
Now, as you have to multiply the numbers with the lowest power, in this case, it would be multiplying 2 with nothing else. So, the answer would be 2, which is the highest common factor.
HCF by Division Method
To find the highest common factor in this method, you will initially need to divide the largest number by the smallest number in the given set. Following this, use the divisor as the new dividend and the remainder as the new divisor. Repeat this process until you reach a remainder of 0. The last divisor you have used in this calculation will be the HCF of the given set of numbers.
LCM by Prime Factorization Method
To find the LCM, you will have to re-write the provided numbers by performing prime factorisation to ascertain their prime factors. Once this is done, list the prime factors and multiply the common values with the highest power. The product of this will be the lowest common multiple of your set of numbers.
For example, find the LCM of 40 and 24 with the prime factorisation method.
To solve this, you would first find the prime factors of both numbers,
40 = 2 x 2 x 2 x 5 = 23 x 5
24 = 2 x 2 x 2 x 3 = 23 x 3
So, in this case, you would multiply two, which has the highest power of 3, with the other prime factors, which are 5 and 3.
2 x 2 x 2 x 3 x 5 = 120 = LCM
LCM by Division Method
Using the division method, you must divide the given numbers by a common prime number. This should be repeated until you reach a point where you are left with a prime number or one as the remainder. After this, multiply all the divisors and the remaining number together, and the product will be the lowest common multiple.
Are There LCM and HCF Formulas?
Due to the different methods to solve questions for the HCF and LCM, you might want to memorise various LCM and HCF formulas to make them easier to perform. That being said, unlike many other calculations, there aren’t any defined formulas for these calculations. Instead, a great tip is to remember the names of the methods as they provide clues to solving them.
- Prime Factorisation Methods = Prime Factorisation Of Numbers
- Division Method = Division Of Numbers
Conclusion
Using these methods, you can find the LCM and HCF of most numbers without any issues. This should make your preparation for SSC much easier and help you improve your ability for prime factorisation and calculation simultaneously. That being said, be sure to practice and understand the methods properly to avoid any mistakes.
