Question

The HCF and LCM of 48, 72 and 60 are

• A. 24, 144
• B. 12, 720
• C. 720, 12
• D. 12, 144

Answer 1

The Correct Option is B

To find the HCF (Highest Common Factor) and LCM (Least Common Multiple) of 48, 72, and 60, we first factor each number into prime factors: \[ 48 = 2^4 \times 3, \quad 72 = 2^3 \times 3^2, \quad 60 = 2^2 \times 3 \times 5 \] HCF (Highest Common Factor): The HCF is found by taking the lowest power of the common prime factors. The common prime factors are 2 and 3, and the lowest powers are \(2^2\) and \(3^1\). Therefore, the HCF is: \[ HCF = 2^2 \times 3 = 12 \] LCM (Least Common Multiple): The LCM is found by taking the highest power of each prime factor. The prime factors are 2, 3, and 5. The highest powers are \(2^4\), \(3^2\), and \(5^1\). Therefore, the LCM is: \[ LCM = 2^4 \times 3^2 \times 5 = 16 \times 9 \times 5 = 720 \] Thus, the HCF is \(12\) and the LCM is \(720\).

The correct option is (B): \(12, 720\)