Final answer:
The other number can be found using the relationship GCD × LCM = a × b, which results in the other number being 55 when the GCD is 11, the LCM is 330, and one of the numbers is 66.
Step-by-step explanation:
The student has provided the Greatest Common Divisor (GCD) and the Least Common Multiple (LCM) of two numbers, as well as one of the numbers itself, and asks for the other number. The relationship between the GCD, LCM, and the two numbers (let's call them a and b) is given by the formula: GCD(a, b) × LCM(a, b) = a × b. We're told that the GCD is 11, the LCM is 330, and one of the numbers (a) is 66. To find the other number (b), we can arrange the formula to solve for b: b = (GCD × LCM) / a.
To find the other number:
- Substitute the known values into the formula: b = (11 × 330) / 66.
- Calculate the product of the GCD and LCM: 11 × 330 = 3630.
- Divide the product by the known number: 3630 / 66 = 55.
Therefore, the other number is 55.