How many numbers up to 450 are divisible by 4, 6 and 8 together?

A. 19
B. 18
C. 17
D. None of these

Answer

Correct Answer: B. 18

Detail about MCQs

To find the numbers up to 450 that are divisible by 4, 6, and 8 together, we need to find the numbers that are divisible by the least common multiple (LCM) of 4, 6, and 8.

The LCM of 4, 6, and 8 is the smallest number that is divisible by all three numbers, which can be found by calculating the prime factorization of each number:

  • 4 = 2^2
  • 6 = 2 * 3
  • 8 = 2^3

To find the LCM, we take the highest power of each prime factor that appears in any of the numbers: 2^3 * 3 = 24.

So, any number that is divisible by 24 is also divisible by 4, 6, and 8.

Now, to find how many numbers up to 450 are divisible by 24, we divide 450 by 24:

450 ÷ 24 = 18 with a remainder of 18.

So, there are 18 whole multiples of 24 up to 450.

Therefore, the correct answer is B. 18.

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