Question

What is the difference between LCM and HCF of $20,30,40$?

Answer 1

Step 1. Find the LCM of $20,30,40$

Prime factorization of $20=2\times 2\times 5$

Prime factorization of $30=2\times 3\times 5$

Prime factorization of $40=2\times 2\times 2\times 5$

$$\begin{gathered} \mathrm{LCM}\left(20,30,40\right)=2\times 2\times 2\times 5\times 3 \\ =120 \end{gathered}$$

Step 2. Find the HCF of $20,30,40$.

$$\begin{gathered} \mathrm{HCF}\left(20,30,40\right)=2\times 5 \\ =10 \end{gathered}$$

Step 3. Difference between lcm and HCF of $20,30,40$.

Now, difference is

$$\begin{gathered} \mathrm{LCM}-\mathrm{HCF}=120-10 \\ =110 \end{gathered}$$

Thus, difference between lcm and HCF of $20,30,40$ is $110$.