Hey Guys, Are you facing difficulty while solving HCF and LCM problems? Don’t worry, just follow the post and your all difficulties and doubt will be cleared. Here we have mentioned the basic concept of HCF and LCM along with the shortcut tricks to solve all problems.
Why you should learn HCF and LCM?
If you want to be strong in Mathematics and Aptitude, then you have to be strong in HCF and LCM. HCF and LCM are two backbones of Mathematics. As like you need food to make your body function similarly you have to be strong in LCM and HCF to do solve further mathematics. Because you will use this concept in every step of mathematics like Addition, Substraction, Calculus and other solutions.
What is the concept of Factor?
A bunch of numbers multiplied with each other to form a new number is called factor of that new number.
How to calculate the factor of a number?
Let us understand the concept of factor by taking an example:
Example: Find the factor of 24, 25, 28?
Solution: (i) 24= 2 × 2 × 2 × 3
(ii) 25= 5 × 5
(iii) 28 = 2 × 2 × 7
I think the concept of factor is now cleared.
HCF (Highest Common Factor)
HCF of two or more number is a number which divides each and every number exactly. In genral, we can say that the highest common factors between two or more numbers is called HCF of that number.
Common factor is the factors which are present in both the number is called common factor.
Example: Factor of 6= 2, 3
& 12= 2, 2, 3
So we can say that 2 and 3 are the common factor of both the number.
Example of HCF of two numbers
Q. Calculate the HCF of 6 and 12
Factor of 6= 2 , 3
Factor of 12= 2, 2, 3
Here Common factors are 2 and 3
So HCF = 2 × 3=6
Q. Find the HCF of 6 and 14?
LCM (Least common multiple)
LCM is a least number which is divisible by all the given numbers. In other words, we can say that LCM is the product of highest factor of a given number.
Example: LCM of 6, 8
6= 2, 3
8= 2, 2, 2
So LCM= 2 × 2 × 2 × 3= 24
Example 2: LCM of 6 and 14?
- HCF × LCM = Product of numbers
HCF and LCM of Decimal Number
Lets take an example to understand How to find the HCF and LCM of Decimal number.
Q. Find the GCD and LCM of the number 0.6, 0.18 and 1.2?
Step-1: First of all check what is the number of digits after ‘.’ (Dot) point.
Step-2: Convert all the digits after ‘.’ point into two digits. If one digit is present, put ‘0’ to make it two digits.
Step-3: Remove ‘.’ dot from all the number.
60 18 120
Step-4: Calculate HCF of 60, 18, 120
Step-5: Calculate LCM of 60, 18, 120
So LCM= 2 × 3 × 2 × 5 × 3 × 2=360
Step-6: Divide the calculated result by 100 to calculate HCF and LCM of the given numbers.
LCM= 360/100= 3.60
HCF and LCM of Fraction
Q. Find the LCM and GCD of ?
HCF and LCM of Power of a Number
Q. Find the GCM and LCM of 6², 6¹³, 6 ^18, 6^19? (^=Power)
Solution: HCF= 6²
LCM = 6^19
Q. Find the LCM and GCM of 3^-2 , 3^-12, 3^-23, 3 ^-32? (^=Power)
Solution: HCF= 6²
LCM = 6^19
HCF and LCM of Power of Polynomial
Q. What is the LCM and HCF of 2ab, 6a²b, 8a²b² ?
Solution: Given Expression= 2ab, 6a²b, 8a²b²
We can write 2ab, 6a²b, 8a²b²= 2ab, 2 × 3 a²b, 2³a²b²
So our final HCF= 2ab
and LCM= 2³a²b²
Q. What is the LCM and HCF of x² – xy, x – y, 3x – 3y, x²- 2xy + y² ?
Solution: Given Expression= x² – xy, x – y, 3x – 3y, x²- 2xy + y
We can write as x( x – y), x – y, ( x – y)²
So our final HCF= x – y
and LCM= x ( x-y)²
I think your concept regarding this topic is cleared. If something is missing in this post, then kindly let me know about that.