Using prime factorization find the HCF and LCM of 21 28 36 and 45

To find the LCM (Least Common Multiple) of 21, 28, 36, and 45, we need the least number which is exactly divisible by all the numbers 21, 28, 36, and 45 without leaving any remainder.

Answer: LCM of 21, 28, 36, and 45 is 1260 and the HCF of 21, 28, 36, and 45 is 1

The largest possible number which divides the given numbers exactly without any remainder is called the HCF (Highest Common Factor).

Explanation:

We will use the prime factorization method to calculate the LCM of 21, 28, 36, and 45.

Represent 21, 28, 36, and 45 as a product of its prime factors.

Prime factorization of 21 is 3 × 7 = 3¹ × 7¹

Prime factorization of 28 is 2 × 2 × 7 = 2² × 7¹

Prime factorization of 36 is 2 × 2 × 3 × 3 = 2² × 3²

Prime factorization of 45 is 3 × 3 × 5 = 3² × 5¹

Now the LCM is the multiplication of the highest powers of each prime factor.

LCM = 2² × 3² × 5¹ × 7¹

= 4 × 9 × 5 ×7

= 1260

So, the LCM of 21, 28, 36, and 45 is 1260

There's no common factor in the prime factorization of 21, 28, 36, and 45.

So, HCF of 21, 28, 36, and 45 is 1.

Therefore, the LCM of 21, 28, 36, and 45 is 1260 and the HCF of 21, 28, 36, and 45 is 1.