How many two-digit positive intergers are multiples of both 2 and 5?
Is the correct answer 9?
Right!
Yeah!
To determine the number of two-digit positive integers that are multiples of both 2 and 5, we can use the concept of the least common multiple (LCM) of the two numbers. The LCM of 2 and 5 is equal to the product of the two numbers since they are prime and have no common factors.
LCM(2, 5) = 2 * 5 = 10
Now, we need to count the number of two-digit positive integers that are divisible by 10. A two-digit positive integer starts from 10 and ends at 99.
To find the number of integers in a given range that are divisible by a certain number, we use the formula:
Number of integers = (largest integer - smallest integer) / common difference + 1
In this case, the smallest integer is 10, the largest integer is 99, and the common difference is 10 (since we are considering multiples of 10).
Number of two-digit integers divisible by 10 = (99 - 10) / 10 + 1 = 89 / 10 + 1 = 8 + 1 = 9
So, the correct answer is 9.