Find the HCF and LCM of 24 and 60

1. **Prime Factorization** - For \( 24 \): \( 24 = 2 \times 2 \times 2 \times 3 = 2^3 \times 3 \) - For \( 60 \): \( 60 = 2 \times 2 \times 3 \times 5 = 2^2 \times 3 \times 5 \) 2. **HCF (Highest Common Factor)** - Identify the common prime factors with the smallest exponent: - For \( 2 \): the minimum exponent is \( 2^2 \) (from \( 60 \)). - For \( 3 \): both have \( 3^1 \). - Multiply these together: \( \text{HCF} = 2^2 \times 3 = 4 \times 3 = 12 \) 3. **LCM (Least Common Multiple)** - Take each prime factor with the highest exponent from either number: - For \( 2 \): the maximum exponent is \( 2^3 \) (from \( 24 \)). - For \( 3 \): \( 3^1 \). - For \( 5 \): \( 5^1 \) (only present in \( 60 \)). - Multiply these together: \( \text{LCM} = 2^3 \times 3 \times 5 = 8 \times 3 \times 5 = 120 \) 4. **Final Answer** - \( \text{HCF}(24, 60) = 12 \) - \( \text{LCM}(24, 60) = 120 \)