Final answer:
To find the HCF of 300 and 450, prime factorize each number and find the product of the lowest power of each common factor. The HCF is 30. To find the LCM, use the formula (300 x 450) / HCF to get 4500.
Step-by-step explanation:
To find the highest common factor (HCF) of 300 and 450, we need to find the largest number that divides both 300 and 450 without leaving a remainder. We can use the method of prime factorization to do this.
The prime factorization of 300 is 2 x 2 x 3 x 5 x 5. The prime factorization of 450 is 2 x 3 x 3 x 5 x 5.
The common factors of 300 and 450 are 2, 3, and 5. To find their HCF, we take the product of the lowest power of each common factor: HCF = 2 x 3 x 5 = 30.
To find the least common multiple (LCM) of 300 and 450, we need to find the smallest number that is divisible by both 300 and 450. We can use the formula: LCM = (300 x 450) / HCF. Substituting the values, we get LCM = (300 x 450) / 30 = 4500.