Problem: The smallest positive integer x for which 1260x=N3, where N is an integer, is:
Answer Choices:
A. 1050
B. 1260
C. 12602
D. 7350
E. 44100
Solution:
1260x=(2⋅2⋅3⋅3⋅5⋅7)x. For the smallest integer cube the exponent of each different prime factor must be 3. Therefore, x=2⋅3⋅52⋅72=7350.