A 20-pound carton that measures 24 × 18 × 12 inches bills at 38 pounds on a 139 divisor and 32 pounds on 166. The box is not heavy. It is mostly air, and the divisor is the carrier's price for air.
The divisors, and where each one is written
FedEx publishes 139 on "What is Dimensional Weight? | FedEx": multiply length, width and height in inches, round each measurement to the nearest whole inch, and divide by 139 for U.S., Puerto Rico and international shipments. That page does not say what to do with the fraction of a pound.
UPS publishes two divisors on "Shipping Dimensions and Weight | UPS - United States", in the answer to "What is dimensional weight and how do I calculate it?": "The divisor varies by rate type: 139 for Daily Rates; 166 for Retail Rates." The same page says to increase any fraction to the next whole pound.
Those are the only two numbers this page uses, and both come off the carrier's own page rather than a reseller's summary.
139 is a density, not an arbitrary number
Divide 1,728, the number of cubic inches in a cubic foot, by the divisor, and the divisor turns into pounds per cubic foot. 1,728 ÷ 139 = 12.43 pcf. 1,728 ÷ 166 = 10.41 pcf.
Put those two against the thirteen density bands and they land in named classes. 12.43 pcf sits inside class 85, which covers 12 to 15 pcf. 10.41 pcf sits inside class 92.5, which covers 10 to 12.
So a parcel billed on a 139 divisor is being priced as if every cubic foot of it weighed 12.43 pounds, whether it does or not. A 166 divisor prices the same cubic foot at 10.41 pounds. The parcel carrier has written the density assumption into the divisor; the LTL carrier makes you measure it.
The same carton, both ways
The carton above holds 5,184 cubic inches, which is 3.00 cubic feet. At 20 pounds on the scale it runs 6.67 pcf, and no LTL pricing would call that dense. Billed as a parcel at 139 it becomes 38 pounds, which is an implied 12.67 pcf.
Now put the freight on a pallet instead. 620 pounds of cartons on a 48 × 40 pallet stacked 48 inches is 48 × 40 × 48 = 92,160 cubic inches, 53.33 cubic feet, and 620 ÷ 53.33 = 11.63 pcf, class 92.5. Add the 40-pound pallet and it is 660 ÷ 53.33 = 12.38 pcf, class 85.
Both roads end up near 12 pcf. The parcel route arrives there by dividing your cubic inches by 139; the LTL route arrives there by measuring the pallet and looking the density up in the bands. Whether the 40-pound pallet belongs in the weight at all is on the page about whether the pallet weight counts.
The two pages disagree with themselves on rounding
FedEx says round each measurement to the nearest whole inch. UPS says two things. Its measuring section says to round up, with an example that 1.01 to 1.99 becomes 2. Its dimensional weight answer says to round each measurement to the nearest whole number. Those are different instructions for the same tape measure.
The difference is not academic. A carton measuring 24.4 × 18.4 × 12.4 inches is 24 × 18 × 12 rounded to nearest, 5,184 cubic inches, 38 pounds at 139. Rounded up it is 25 × 19 × 13, 6,175 cubic inches, 45 pounds at 139. Seven pounds of billed weight created by four tenths of an inch.
What to do with this
Measure at the longest point of each side, write the three numbers down before you choose the box, and run step two both ways. If the dim weight beats the scale weight by more than the cost of a smaller carton, the carton is the cheaper answer. If the goods are going on a pallet anyway, the divisor stops mattering and the pcf starts, because LTL prices the pallet and not the parcel.