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(a, b), is the smallest positive integer that is divisible by both a and b. If either a or b is 0, LCM(a, b) is defined to be zero.
Points of Difference 
HCF

LCM

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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)



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



Given a, b, c,…. are infinate positive integers then



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