For better understanding of the concept

**LCM**(Lowest Common Multiple) and HCF (Highest Common Factor) we need to recollect terms multiples and factors. Let’s learn about LCM, HCF and relation between HCF and LCM of natural numbers.**Multiples:**A multiple is any number which is exactly divisible by a given number. Ex: 3, 6,9,12, etc are the multiples of 3.

**Factors**: A factor is a number which divides any given number without leaving remainder. Ex: 2,3,4,6,8,12 are the factors of 24.

**Lowest Common Multiple (LCM):**The least or smallest common multiple of any two or more given natural numbers are termed as LCM. For example, LCM of 10, 15, and 20 is 60.

**Highest Common Factor (HCF):**The largest or greatest factor common to any two or more given natural numbers is termed as

**HCF**of given numbers. Also known as GCD (Greatest Common Divisor).For example, HCF of 4, 6 and 8 is 2.

Here, highest common factor of 4, 6 and 8 is 2.

Both

**HCF and LCM**of given numbers can be find by using two methods; they are division method and prime factorization.#####
**PROPERTIES OF HCF AND LCM**

**Property 1:**The product of LCM and HCF of any two given natural numbers is equivalent to the product of the given numbers.

LCM x HCF = Product of the Numbers

Suppose A and B are two numbers, then.

LCM (A&B) x HCF (A&B) = A x B

**Example 1:**Prove that:

LCM (9 & 12) x HCF (9&12) = Product of 9 and 12

**Solution:**LCM and HCF of 9 and 12:

**Property 2:**HCF of co-prime numbers is 1. Therefore LCM of given co-prime numbers is equal to the product of the numbers.

LCM of Co-prime Numbers = Product Of The Numbers

**Example 2:**8 and 9 are two co-prime numbers. Using this numbers verify,

LCM of Co-prime Numbers = Product Of The Numbers

**Solution:**LCM and HCF of 8 and 9:

**Property 3:**H.C.F. and L.C.M. of Fractions