Find the lcm and hcf of6,10 and 20

• For 6:

$$6 = 2 \times 3$$

• For 10:

$$10 = 2 \times 5$$

• For 20:

$$20 = 2 \times 2 \times 5 = 2^2 \times 5$$

The HCF is the product of the common prime factors raised to the lowest power they appear in any of the factorizations.
The only prime factor common to all three numbers (6, 10, 20) is 2.
The lowest power of 2 is $2^1$.

$$\text{HCF}(6, 10, 20) = 2^1 = 2$$

The LCM is the product of all unique prime factors raised to the highest power they appear in any of the factorizations.
The unique prime factors are 2, 3, and 5.

• Highest power of 2: $2^2$ (from 20)
• Highest power of 3: $3^1$ (from 6)
• Highest power of 5: $5^1$ (from 10 and 20)

$$\text{LCM}(6, 10, 20) = 2^2 \times 3^1 \times 5^1 = 4 \times 3 \times 5 = 60$$

The HCF is $\boxed{2}$ and the LCM is $\boxed{60}$.