To create packages containing equal numbers of lubricant cans and coolant bottles, we need to find the greatest common divisor of 150 and 80.
The prime factorization of 150 is 2 x 3 x 5 x 5, while the prime factorization of 80 is 2 x 2 x 2 x 2 x 5.
The common factors are 2 and 5, so the GCD is 2 x 5 = 10.
Therefore, the largest number of packages that can be created without any leftover cans or bottles is the total number of cans and bottles divided by the GCD:
(150 + 80) / 10 = 23
So the car service center can create 23 packages containing equal numbers of lubricant cans and coolant bottles.
Answers & Comments
To create packages containing equal numbers of lubricant cans and coolant bottles, we need to find the greatest common divisor of 150 and 80.
The prime factorization of 150 is 2 x 3 x 5 x 5, while the prime factorization of 80 is 2 x 2 x 2 x 2 x 5.
The common factors are 2 and 5, so the GCD is 2 x 5 = 10.
Therefore, the largest number of packages that can be created without any leftover cans or bottles is the total number of cans and bottles divided by the GCD:
(150 + 80) / 10 = 23
So the car service center can create 23 packages containing equal numbers of lubricant cans and coolant bottles.