Determine the hcf and lcm 28 and 72

General
1

determine the hcf and lcm 28 and 72

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What is the HCF (Highest Common Factor) and LCM (Least Common Multiple) of 28 and 72?

Answer:
To find the HCF and LCM of two numbers, 28 and 72 in this case, we can follow these steps:

Step 1: Prime Factorization
Find the prime factors of both numbers. Prime factors are the prime numbers that multiply together to give the original number.

Prime factorization of 28:
28 = 2 x 2 x 7

Prime factorization of 72:
72 = 2 x 2 x 2 x 3 x 3

Step 2: HCF (Highest Common Factor)
To find the HCF, we need to find the highest common factor of the two numbers. The HCF is the largest number that divides both 28 and 72 without leaving a remainder.

The common factors of 28 and 72 are 1, 2, and 4.

However, the highest common factor is 4 because it is the largest number that divides both 28 and 72 without any remainder.

Therefore, the HCF of 28 and 72 is 4.

Step 3: LCM (Least Common Multiple)
To find the LCM, we need to find the smallest common multiple of the two numbers. The LCM is the smallest number that is divisible by both 28 and 72.

To find the LCM, we can use the formula:

LCM = (Number 1 x Number 2) / HCF

Substituting the values, we get:

LCM = (28 x 72) / 4 = 2016

Therefore, the LCM of 28 and 72 is 2016.

In conclusion, the HCF of 28 and 72 is 4, and the LCM is 2016.