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 is the only common multiple with those three numbers.
24 and 48
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
48, 96
They are 4, 8 and 12
8 = 2310 = 2*512 = 22*3LCM = 3*5*8 = 120So the two first common multiples of 8, 10, and 12 are 120 and 240.
The first three common multiples of 8 and 12 are 24, 48, and 72.
2, 4, 6, 8, 10, 12, 14
2, 4, 6, 8, 10, 12.
2, 4, 6, 8, 10, 12