The first thing you should notice is that both 8 and 12 are evenly divisible by 2. This means that any common multiples of 8 and 12 will also be multiples of 2. So we only really need to find the first three common multiples of 8 and 12.
First common multiple: 24
8 * 3 = 24
12 * 2 = 24
(2 * 12 = 24)
Second common multiple: 48
8 * 6 = 48
12 * 4 = 48
(2 * 24 = 48)
Second common multiple: 72
8 * 9 = 72
12 * 6 = 72
(2 * 36 = 72)
2, 4, 6, 8, 10, 12
If ordered by size, only every other multiple of 2 is a multiple of 4. All multiples of 4 are multiples of 2.
Multiples of 2 are 2, 4, 6, 8, 10, 12, 14, 16, 18, . . . Multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72, . . .
The first five multiples of 4 are 4, 8, 12, 16 and 20. For them to be common, they need to be compared to another set of multiples.
4, 8, 12, 16
4, 8 and 12 are the first 3 common multiples of 2 and 4
2 8 12
All multiples of 8 are also multiples of 2, but not all multiples of 2 are multiples of 8.
2, 4, 6, 8, 10, 12
6 8 9 2 5 7
They are 4, 8 and 12
48, 96
8 = 2310 = 2*512 = 22*3LCM = 3*5*8 = 120So the two first common multiples of 8, 10, and 12 are 120 and 240.
2, 4, 6, 8, 10, 12, 14
2, 4, 6, 8, 10, 12
2, 4, 6, 8, 10, 12.
The first three common multiples of 8 and 12 are 24, 48, and 72.