Prime Factorization Math Example 2

Solution

1. 1
   Factor $180 = 2^2 \times 3^2 \times 5$ and $252 = 2^2 \times 3^2 \times 7$.
2. 2
   $\gcd$: take the minimum exponent for each shared prime: $2^{\min(2,2)} \times 3^{\min(2,2)} = 2^2 \times 3^2 = 4 \times 9 = 36$.
3. 3
   $\text{lcm}$: take the maximum exponent for each prime that appears: $2^2 \times 3^2 \times 5 \times 7 = 36 \times 35 = 1{,}260$.
4. 4
   Verify: $\gcd \times \text{lcm} = 36 \times 1{,}260 = 45{,}360 = 180 \times 252$. ✓