1st VS 2nd

HCF vs LCM

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HCF : In mathematics, the highest common factor (hcf), also known as the greatest common factor (gcf), or greatest common divisor (gcd), of two or more integers (at least one of which is not zero), is the largest positive integer that divides the numbers without a remainder.

LCM : In arithmetic and number theory, the least common multiple (also called the lowest common multiple or smallest common multiple) of two integers a and b, usually denoted by LCM(ab), is the smallest positive integer that is divisible by both a and b. If either a or b is 0, LCM(ab) is defined to be zero.

 

Points of Difference

HCF
LCM
Picture
HCF of 60 and 30
LCM of 30 and 60
Stands for
Highest Common Factor
Least Common Multiple
Definition
The Highest Common Factor (H.C.F) of two (or more) numbers is the largest number that divides evenly into both numbers. In other words the H.C.F is the largest of all the common factors.
The Lowest Common Multiple (L.C.M) is the smallest number that is a common multiple of two or more numbers.
Nature
The HCF is based upon what integer divides evenly into two numbers.
LCM is based upon what integer two numbers share in a list of multiples.
Notation
we denote the highest common factor of two integers a and b as hcf(a,b).
we denote the least common multiple of two integers a and b as lcm( a, b ).
Example using prime factorizations (for 48 and 180)
HCF of 48 and 180
So HCF of 48 and 180 is 2*2*3= 12
LCM of 30 and 60
So LCM of 48 and 180 is 2*2*2*2*3*3*5= 720
Relation for two positive integers a, b
H.C.F = (a*b)/L.C.M
L.C.M = (a*b)/H.C.F
Realation b/w HCF and LCM
The H.C.F of two or more numbers is a factor of their L.C.M
The H.C.F of two or more numbers is a factor of their L.C.M
For three positive integers, a, b, c
H.C.F ≠ (a*b*c)/L.C.M
L.C.M ≠ (a*b*c)/H.C.F
Given a, b, c are positive integers then
Relation of HCF, LCM of three numbers
Relation of HCF, LCM of three numbers
Given a, b, c,…. are infinate positive integers then
Relation of HCF, LCM of infinate numbers
Relation of HCF, LCM of infinate numbers

So that was all for HCF vs LCM. Don’t forget to share the knowledge with your friends.


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