Divide the LCM of 160,18,24 by their HCF

$$160 = 16 \times 10 = 2^4 \times (2 \times 5) = 2^5 \times 5^1$$ $$18 = 2 \times 9 = 2^1 \times 3^2$$ $$24 = 8 \times 3 = 2^3 \times 3^1$$

The HCF is found by taking the lowest power of each common prime factor.
The only common prime factor among $160, 18,$ and 24 is 2.
The lowest power of 2 is $2^1$ (from 18).

$$\text{HCF}(160, 18, 24) = 2^1 = 2$$

The LCM is found by taking the highest power of each prime factor present in any of the numbers.

• Highest power of 2: $2^5$ (from 160)
• Highest power of 3: $3^2$ (from 18)
• Highest power of 5: $5^1$ (from 160)

$$\text{LCM}(160, 18, 24) = 2^5 \times 3^2 \times 5^1$$ $$\text{LCM} = 32 \times 9 \times 5$$ $$\text{LCM} = 288 \times 5$$ $$\text{LCM} = 1440$$

$$\frac{\text{LCM}}{\text{HCF}} = \frac{1440}{2}$$ $$\frac{\text{LCM}}{\text{HCF}} = 720$$

The result of dividing the LCM by the HCF is 720.