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A common question that many students come across is how to find the HCF and LCM quickly? This is because HCF and LCM problems are a prominent part of various professional examinations and can help improve your score significantly. So, learning the fastest and simplest way to solve these questions is important.
The solution to these questions is divided into two parts. You can follow simple ways, such as the HCF by prime factorisation or LCM by division method. Or you can use some easier tricks that can help make some questions easier to solve. In this article, we’ll be covering both ways to help you find the most suitable ways to find the HCF and LCM.
How to Find HCF and LCM?
Here are some basic approaches to solving LCM and HCF problems.
LCM by Prime Factorisation Method
To find the LCM using this method, you must rewrite the given numbers using prime factorisation to determine their prime factors. After that, multiply the common values which have the highest power. The lowest common multiple of your set of numbers will be the product of this calculation.
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 2 as it 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
For this, you must divide the provided numbers by a common prime number. This should be done until you’re left with a prime number or 1 as the remainder. Once this is done, multiply all the divisors and the remaining number together. The product of this will be your Lowest Common Multiple.
HCF by Prime Factorisation Method
You must first perform prime factorisation on the given collection of numbers before using this method to get the highest common factor. After completing this and having the prime factors, find the common factors with the lowest power and multiply them. The product of this will be the HCF for your set of numbers.
- 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, 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 determine the highest common factor using this method, you must first divide the largest number by the lowest number in the supplied set. The divisor will now be the new dividend, and the remainder will be the new divisor. Repeat until you have a remainder 0 at the end of the process. At this point, the last divisor that you have used in this calculation will be the HCF of the given set of numbers.
Easy Methods To Find HCF and LCM Quickly
For Finding The HCF
An easy way to find the highest common factor of a set of numbers is to find the difference between a pair of numbers and see if they are divisible by this number. This process is great for smaller numbers and can even work with larger sets with multiple numbers, albeit slightly more tedious.
1. Find the HCF of 16 and 12.
The difference between these two is 4. Now, if you divide both numbers by 4, you will get a remainder of 0, which means they are divisible. So, you can easily and quickly ascertain that the highest common factor is 4.
That being said, keep in mind that this method is more difficult when working with complex or larger numbers.
For Finding The LCM
An easy trick to finding the LCM of a given set of numbers is to look at the largest number and its multiples. This is because the LCM is a multiple of all the numbers in the set, so the largest number will be the easiest to use when calculating the LCM. For example, let’s suppose you have to find the lowest common multiple of 2, 3, 7, and 21.
As the largest number is 21, you can first see if it is divisible by all the numbers in the set. As this is not the case in this question, we will move up to the next multiple of 21, which is 42. When checking for 42, you can see that it is divisible by the complete set of numbers. So, 42 would be your LCM for the set of numbers.
One thing you should keep in mind with this method is that it shouldn’t be used for larger sets of numbers as this will cost you more time.
Conclusion
Using these methods, you can solve HCF and LCM problems easily and quickly. Whether it is following the primary prime factorisation and division methods for larger questions, you will be prepared.
