What is HCF? What is LCM? How you calculate HCF & LCM
of numbers & fractions quickly?
Find out in this short presentation by https://allexammocktest.in
1. What is HCF & LCM ?
HCF (Highest Common Factor) - The HCF of 2 numbers is the largest common factor that
they have.
LCM (Lowest Common Multiple) – The LCM of 2 numbers is the smallest common factor they
they have.
2. Example - 12,20 and 30
See there are only two common factors 1 and 2.
2 is the largest common factor. Similarly, 60 is the smallest common multiple.
So,
The answer is - 2 is the HCF and 60 is the LCM.
3. Tricks to Find Out HCF & LCM Quickly
We shall find out the HCF and LCM of 18, 27 and 30 in 3 quick steps.
Step-1
1. Start by factorizing all three numbers in terms of prime factors
So now there are 3 prime factors - 2, 3 and 5.
4. Step-2
Now we are going to express the above 3 equations in such a way that all 3
of them contains 2, 3 and 5.
Look closely –
5. Step 3
In this last step we shall find both the HCF and LCM –
● For HCF, we take the smallest power of 2, 3 and 5 that is common in the 3
equations and multiply them.
● For LCM, we take the largest power of 2, 3 and 5 in the 3 equations and
multiply them. [Please note that this power does not have to be
common]
6. Practice Problems
Find the HCF and LCM of the following numbers using the method
above. (Try to solve them as fast as you can.) –
1) 12, 28 and 44
2) 132, 246 and 444
3) 121, 605 and 12321
7. HCF and LCM of Fractions
● The formula for finding the HCF of fractions is –
● The formula for finding the LCM of fractions is –
8. The Easy Way To Remember The Formula
The numerators do what you have to do.
The denominators do opposite of what you have to do.
If you need to do HCF, then with the numerators of the fractions find the HCF. Then, find
the LCM with the denominators. Finally form the fraction.
To find the LCM, find the LCM of the numerators. Next, find the HCF of the denominators.
Then form the fraction.
12. Another Important Formula
If M and N are two numbers. And X and Y are the HCF and LCM of M and
N, then –
M x N = X x Y
That means,
The product of two numbers = HCF x LCM
13. Example
Find the smallest such number, which is greater than 3 and when divided by
4, 5, 6 always leaves the same remainder 3.
Solution –
This problem can be solved in 2 steps –
1. Find the smallest number that is divisible by 4, 5, 6. Obviously, the smallest such number is
their LCM = LCM (4, 5, 6) = 60.
2. Add 3 to that number to get the required answer. Therefore the answer is = 60 + 3 = 63.
14. Want To Solve More Questions ?
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