Question

How many positive integers less than 200 are divisible by 2, 3 and 51

Answer 1

To find the number of positive integers less than 200 that are divisible by 2, 3, and 51, we need to find the common multiples of these three numbers. The positive integers less than 200 that are divisible by 2, 3, and 51 are the multiples of 6. There are 33 multiples of 6 less than 200.

Step-by-step explanation:

To find the number of positive integers less than 200 that are divisible by 2, 3, and 51, we need to find the common multiples of these three numbers.

First, we need to find the prime factorization of each number:

• 2 = 2
• 3 = 3
• 51 = 3 * 17

Since the prime factorization of 51 includes a 3, any number that is divisible by 51 is also divisible by 3. Therefore, we only need to consider the numbers that are divisible by both 2 and 3.

To find the common multiples of 2 and 3, we can use the least common multiple (LCM) of 2 and 3, which is 6. So, the positive integers less than 200 that are divisible by 2, 3, and 51 are the multiples of 6. By dividing 200 by 6, we find that there are 33 multiples of 6 less than 200.