Question

Diane tells her mother that the secret number she is thinking of is divisible by 12 and tells her father that it is divisible by 8. If Diane is telling the truth to both of her parents, what is the smallest secret number that Diane could be thinking of?

Answer 1

The smallest secret number Diane could be thinking of that is divisible by both 12 and 8 is 24, which is their least common multiple (LCM).

Step-by-step explanation:

The student asked for the smallest number that is divisible by both 12 and 8. Since 12 and 8 have common factors, we will have to find their least common multiple (LCM). The prime factorization of 12 is 2³ × 3 and the prime factorization of 8 is 2³. The LCM is the highest power of the prime factors involved, which in this case is 2³ × 3 = 24. Hence, the smallest number that Diane could be thinking of is 24, as it is the smallest number divisible by both 12 and 8.