1. The problem is to find the least common multiple (LCM) or \textit{ppcm} of 174 and 406.\n2. Start by finding the prime factorizations of 174 and 406.\n3. Prime factorization of 174:\n$$174 = 2 \times 3 \times 29$$\n4. Prime factorization of 406:\n$$406 = 2 \times 7 \times 29$$\n5. The LCM is found by taking the highest powers of all prime factors in both numbers:\n- For 2: max power is 1\n- For 3: max power is 1 (only in 174)\n- For 7: max power is 1 (only in 406)\n- For 29: max power is 1 (common factor)\n6. Multiply these together to get the LCM:\n$$\text{LCM} = 2 \times 3 \times 7 \times 29$$\n7. Calculate the product:\n$$2 \times 3 = 6$$\n$$6 \times 7 = 42$$\n$$42 \times 29 = 1218$$\n8. Therefore, the \textit{ppcm}(174, 406) is \boxed{1218}.