Two numbers have an HCF of 12 and an LCM of 360…

Step 1. Part (a). The other number is $\dfrac{12 \times 360}{72} = \dfrac{4320}{72} = 60$.

Step 2. Check (a). $72 = 2^3 \times 3^2$ and $60 = 2^2 \times 3 \times 5$. HCF $= 2^2 \times 3 = 12$ and LCM $= 2^3 \times 3^2 \times 5 = 360$.

Step 3. Part (b). The HCF divides both numbers, and each number divides the LCM, so the HCF must divide the LCM. But $150 \div 14$ is not a whole number.