Final answer:
The other number, B, is calculated using the formula B = LCM × HCF / A. With the given values, LCM = 432, HCF = 72, and A = 216, the result is 144. However, this answer is not listed among the options provided.
Step-by-step explanation:
The Least Common Multiple (LCM) and Highest Common Factor (HCF) of two numbers can be used to find the other number if one of the numbers is known.
The relationship between the LCM, HCF, and the two numbers (let's call them A and B) can be described by the formula: LCM × HCF = A × B. Given that the LCM is 432, the HCF is 72, and one of the numbers (A) is 216, we can find the other number (B) by rearranging the formula to B = LCM × HCF / A. Plugging in the values gives us B = 432 × 72 / 216. Simplifying, we get B = 144, which matches none of the given options, indicating a possible error in the question or the provided options.
To find the other number, we can use the formula:
LCM × HCF = Product of the two numbers
Substituting the given values, we have:
432 × 72 = 216 × Other number
Other number = (432 × 72) ÷ 216 = 144