19 feet = 19 × 12 = 228 inches.
0
12
24
36
48
60
72
84
96
108
120
132
144
156
168
180
192
204
216
228
The answer is 10
The correct answer is:
10 times.
Explanation:
We first find the LCM, or least common mulitple, of 8 and 12. To do this, we find the prime factorization of each:
8 = 2*4
4 = 2*2
8 = 2*2*2
12 = 4*3
4 = 2*2
12 = 2*2*3
To find the LCM, we take the common factors and multiply by the uncommon ones. The common factors are 2*2; the uncommon are 2 and 3:
2*2*2*3 = 24
The LCM is 24. This means that every 24 inches, both patterns will repeat.
The patterns are both at the beginning of the design. Then every 24 inches, or 2 feet, both patterns repeat.
19/2 = 9.5
There are an additional 9 times that the patterns repeat; this is 1+9 = 10 total times.
