Question

Determine the HCF and LCM 28 and 72

Answer 1

LCM: 504, HCF: 4

Explanation:

LCM

Here is the prime factorization of 28:

2^2 × 7

And this is the prime factorization of 72:

2^3 × 3^2

When you compare the prime factorization of these two numbers, you want to look for the highest power that each prime factor is raised to. In this case, there are these prime factors to consider: 2, 7, 3

2^3 × 3^2 × 7^1 = 504

Through this we see that the LCM of 28 and 72 is 504.

HCF

Prime factorization of 28 and 72 is 2^2 × 7 and 2^3 × 3^2 respectively. As visible, 28 and 72 have common prime factors. Hence, the GCF of 28 and 72 is 2 × 2 = 4.