The LCM of 12, 15, and 20 is:

**The reasoning** To find the LCM (Lowest Common Multiple), we need the **smallest number that all three numbers divide into evenly**. First, break each number into prime factors: - 12 = 2² × 3 - 15 = 3 × 5 - 20 = 2² × 5 Now, take the **highest power** of each prime that appears: - Highest power of 2: 2² (from 12 or 20) - Highest power of 3: 3¹ (from 12 or 15) - Highest power of 5: 5¹ (from 15 or 20) Multiply them: 2² × 3 × 5 = 4 × 3 × 5 = **60** Check: 60÷12 = 5 ✓, 60÷15 = 4 ✓, 60÷20 = 3 ✓ **Why the wrong options tempt you** **A) 30** – You might think "common multiple" and pick the first one you see, but 30÷20 = 1.5 (not a whole number!). **B) 45** – Looks decent, but 45÷20 doesn't work either. **D) 120** – This IS a common multiple, but not the *lowest*. You probably multiplied all three: 12×15×20 ÷ something, or just picked a "safe" big number. **Quick takeaway** LCM = use prime factorization, then multiply the **highest powers** together—not just any common multiple!