The least common multiple (LCM) of two numbers is the smallest positive integer that is divisible by both. Listing multiples, we get for 6: 6, 12, 18, 24, ... and for 8: 8, 16, 24, 32, ... . The first common multiple is 24. Therefore, the LCM of 6 and 8 is 24.
Option A:
12 is a multiple of 6, but it is not a multiple of 8 since 12 ÷ 8 is not an integer. Therefore, 12 cannot be a common multiple of both numbers. This makes it an invalid candidate for their LCM.
Option B:
18 is a multiple of 6 but not of 8, because 18 ÷ 8 is not integral. Thus, it fails the requirement of being divisible by both numbers. Hence, this option is incorrect.
Option C:
24 is correct because it is the smallest number that appears in the multiples of both 6 and 8. Additionally, 24 ÷ 6 = 4 and 24 ÷ 8 = 3, confirming it is divisible by both. This value is therefore the least common multiple sought in the question.
Option D:
36 is a multiple of 6 but not a multiple of 8 since 36 ÷ 8 does not give an integer. Consequently, it cannot be considered a common multiple of 6 and 8. Thus, 36 is not the LCM in this case.
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