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Building upon previous works, it is shown that two minimal left ideals of thecomplex Clifford algebra $\mathbb{C}\ell(6)$ and two minimal right ideals of$\mathbb{C}\ell(4)$ transform as one generation of leptons and quarks under thegauge symmetry $SU(3)_C\times U(1)_{EM}$ and $SU(2)_L\times U(1)_Y$respectively. The $SU(2)_L$ weak symmetries are naturally chiral. Combining the$\mathbb{C}\ell(6)$ and $\mathbb{C}\ell(4)$ ideals, all the gauge symmetries ofthe Standard Model, together with its lepton and quark content for a singlegeneration are represented, with the dimensions of the minimal ideals dictatingthe number of distinct physical states. The combined ideals can be written asminimal left ideals of $\mathbb{C}\ell(6)\otimes\mathbb{C}\ell(4)\cong\mathbb{C}\ell(10)$ in a way that preserves individually the$\mathbb{C}\ell(6)$ structure and $\mathbb{C}\ell(4)$ structure of physicalstates. This resulting model includes many of the attractive features of theGeorgi and Glashow $SU(5)$ grand unified theory without introducing protondecay or other unobserved processes. Such processes are naturally excludedbecause they do not individually preserve the $\mathbb{C}\ell(6)$ and$\mathbb{C}\ell(4)$ minimal ideals.

The Standard Model particle content with complete gauge symmetries from the minimal ideals of two Clifford algebras