Given that 1 US dollar ($) costs Uganda shillings (Ug.sh) 3,672 and 1 Kenya shilling (Ksh) costs Ug.sh 36, find the cost of 1 US dollar in Kenya shillings.

Given that $1 \text{ Ksh} = 36 \text{ Ug.sh}$, we can find the value of $1 \text{ Ug.sh}$ in Ksh.

$$1 \text{ Ug.sh} = \frac{1}{36} \text{ Ksh}$$

Given that $1 \text{ US dollar} = 3,672 \text{ Ug.sh}$.
Substitute the value of $1 \text{ Ug.sh}$ from Step 1 into this equation.

$$1 \text{ US dollar} = 3,672 \times \left(\frac{1}{36} \text{ Ksh}\right)$$

$$1 \text{ US dollar} = \frac{3,672}{36} \text{ Ksh}$$ $$1 \text{ US dollar} = 102 \text{ Ksh}$$

The cost of 1 US dollar in Kenya shillings is $\boxed{\text{102 Ksh}}$.