Can they be the same number?

$138600=2^3\cdot3^2\cdot5^2\cdot7\cdot11$

$2668050=2\cdot3^2\cdot5^2\cdot7^2\cdot11^2$

Any number of 5's,7's and 11's does not change the fact that there is a different number of 2's.

Since we can only change how many times the number's factors have 5, 7, and 11, we want to know what the remaining number is after dividing by 5, 7, and 11 as much as you can, since that shows the factors you can't change. 138600 can be factored into 5 * 5 * 7 * 11 * 72 and 2668050 into 5 * 5 * 7 * 7 * 11 * 11 * 18. While you can change the amount of 5's, 7's, and 11's in the number, you can't change the 72 and 18, so the answer is no. If the number left over after factoring out the 5's, 7's, and 11's were the same for both numbers, the answer would be yes.