Method 1 (Plugging in and is the quickest)

Using your calculator, the quickest solution will be plugging in the answer choices from the least to the largest:

Choice F: $\frac{60}{70}=0.8571$ and therefore eliminated;

Choice G: $\frac{220}{70}=3.1428$ and therefore eliminated;

Choice H: $\frac{630}{60}=10.5$ and therefore eliminated;

Choice J: $\frac{1260}{60}=21$, $\frac{1260}{70}=18$, $\frac{1260}{90}=14$ and therefore is the answer.

Method 2 (LCM by Division Method)

Therefore, LCM of 60, 70 and 90 = 10 \times 3 \times 2 \times 7 \times 3 = 1,260