Select the correct answerIf both 112 and 33 are factors of the number a x 43 x 62 x 1311, then what is the smallest possible value of 'a'?

To find the smallest possible value of 'a', we need to ensure that 'a' includes all the prime factors of both 112 and 33 that are not already included in 43, 62, and 1311.

First, let's find the prime factors of 112, 33, 43, 62, and 1311.

• 112 = 2^4 * 7
• 33 = 3 * 11
• 43 = 43 (it's a prime number)
• 62 = 2 * 31
• 1311 = 1311 (it's a prime number)

Now, let's see which prime factors of 112 and 33 are not included in 43, 62, and 1311.

• The prime factors of 112 are 2 and 7. 2 is included in 62, but 7 is not included in any of the other numbers. So, 'a' must include 7.
• The prime factors of 33 are 3 and 11. Neither 3 nor 11 is included in any of the other numbers. So, 'a' must include 3 and 11.

Therefore, the smallest possible value of 'a' is the product of 7, 3, and 11, which is 231.