Final answer:
The LCM (Least Common Multiple) of the given numbers 16, 42, and x is 2016. The prime factorization method is used to find the LCM, and the highest exponents of the common factors are chosen. Therefore, x = 36 is the correct option.
Step-by-step explanation:
The LCM (Least Common Multiple) of the given numbers can be found by breaking down the numbers into their prime factors and selecting the highest exponent for each prime factor.
Prime factorization of 16: 2^4
Prime factorization of 42: 2 * 3 * 7
Prime factorization of 2016: 2^5 * 3^2 * 7
To find the LCM, we choose the highest exponent for each prime factor, which gives us LCM = 2^5 * 3^2 * 7 = 2016.
Therefore, the value of x is 2016. The correct option is d. x = 36.