Final answer:
To find the LCM of 6 and an unspecified number q, list the multiples of both numbers and identify the smallest common number. The multiples of 6 include numbers like 6, 12, 18, and so on. We cannot list the multiples of q without knowing its value.
Step-by-step explanation:
A student has asked how to write the multiples of 6 and an unspecified number q, and to circle the Least Common Multiple (LCM). Let's start with the number 6. The multiples of 6 are numbers that can be divided evenly by 6. Starting from 6 and going onwards, these multiples include 6, 12, 18, 24, 30, and so forth, increasing by 6 each time. However, since we do not know the value of q, we cannot list its multiples specifically.
To find the LCM of two numbers, you list the multiples of both numbers and identify the smallest number that appears in both lists. In the case with number 6, once we know the value of q, we can list out its multiples and compare to find the LCM. If q is also a whole number, its multiples would start with q, 2q, 3q, and so on. The LCM is where the multiples of 6 and q have a common value.
For example, if q was 8, the multiples of 8 would be 8, 16, 24, 32, etc., and the smallest common multiple with 6 would be 24, which is our LCM.