Numbers divisible by both 6 and 8 are multiples of their least common multiple (LCM).
Finding the LCM of 6 and 8
To find the numbers divisible by both 6 and 8, we first determine their least common multiple (LCM). The prime factorization of 6 is 2 x 3, and the prime factorization of 8 is 2 x 2 x 2 (or 2³). The LCM is found by taking the highest power of each prime factor present in the numbers: 2³ x 3 = 24.
Numbers Divisible by Both 6 and 8
Therefore, any number divisible by both 6 and 8 must be a multiple of 24. This includes:
- 24
- 48
- 72
- 96
- 120
- and so on...
As noted in the provided references, numbers like 48 and 72 are examples of numbers divisible by both 6 and 8. The reference also highlights that 3072 is divisible by both 6 and 8 because it's a multiple of 24 (3072 = 24 x 128). Another reference mentions that any number divisible by both 6 and 8 must be a multiple of 24.
