what is the difference between HCF and LCM?

what is prime factorization?

The

**HCF**of two or more numbers is the largest common factor of the given numbers. It is the smallest number which divides the two or more given numbers.The

**LCM**of two or more numbers is the smallest number that is a common multiple of two or more numbers. It is the smallest number which is divisible by two or more given numbers.Consider two numbers 120 and 144.

Prime factorization of 120 = 2 × 2 × 2 × 3 × 5

Prime factorization of 144 = 2 × 2 × 2 × 2 × 3 × 3

HCF of 120 and 144 = 2 × 2 × 2 × 3 = 24. 24 is the smallest number which divides both 120 and 144.

LCM of 120 and 144 = 2 × 2 × 2 × 2 × 3 × 3 × 5 = 720. 720 is the smallest number which is divisible by both 120 and 144.

**If a number is expressed as a product of its factors, all of which are prime numbers, then such factorization is known as prime factorization.**

Prime factorization of 135 = 3 × 3 × 3 × 5

**
**