Balance the decomposition of potassium chlorate: KClO$_3$ $\xrightarrow{\Delta}$ KCl + O$_2$. The correct coefficients (KClO$_3$, KCl, O$_2$) are:

1. Oxygen appears as 3 atoms in one KClO$_3$ but as 2 atoms in O$_2$; the LCM of 3 and 2 is 6. 2. Put 2KClO$_3$ to get 6 O atoms on the left, and 3O$_2$ to get 6 O atoms on the right. 3. This makes 2 K and 2 Cl on the left, so place 2KCl on the right to match: 2KClO$_3$ $\longrightarrow$ 2KCl + 3O$_2$. 4. Check: K = 2, Cl = 2, O = 6 on both sides. The 1,1,1 and 1,1,3 sets leave O unequal, and 2,2,1 gives only 2 O on the right, so they are wrong. _Source: Balbharati (Maharashtra Board) Class 10 Science & Technology, Ch 3 "Chemical Reactions and Equations", p.50_