Difference between HCF and LCM
The difference between the concept of HCF and LCM is given in the following table:
| HCF |
LCM |
| The full form of HCF is Highest Common Factor. |
The full form of LCM is Least Common Multiple. |
| HCF is the largest of all the common factors of the given numbers. |
LCM is the smallest of all the common multiples of the given numbers. |
| HCF of given numbers cannot be greater than any of them. |
LCM of given numbers cannot be smaller than any of them. |
HCF and LCM Relation:
The multiplication of common prime factors of given numbers with the least exponential powers is the HCF of two numbers or more numbers. For example, The HCF of 12 and 20 is 4.
Prime factors of 12 = 2 × 2 × 3
Prime factors of 20 = 2 × 2 × 5
HCF is 2 × 2 = 4
The LCM or the least common multiple is the smallest natural number which is a multiple of two or more numbers. For example, the LCM of 12 and 20 is 60.
Multiples of 12 = 12, 24, 36, 48, 60, 72, 84 and so on.
Multiples of 20 = 20, 40, 60, 80 and so on.
LCM of 12 and 20 is 60.
HCF and LCM of two numbers are related to each other as well as with the given numbers.
For any two numbers a and b, HCF (a, b) × LCM (a, b) = a × b.
