I used PRIME factors:
10: 2 and 5
14: 2 and 7
18: 2 and 3
So then I multiplied 10x14x18 = 2,520
Then I took the factor of that to figure out the least common multiple of the largest number that I could divide the PRIME factors into evenly (2, 3, 5, and 7):
2,520
/ \
2 1,260
/ / \
2 2 630 (divides evenly by 2,3,5,7)
/ / / \
2 2 2 315 (315 does not work because 2 does not divide into it evenly)