The LCM and HCF of the numbers $42$ and $49$ are in the ratio of

Step 1: Find the Prime Factorization of the numbers.
$$42=2\times 3\times 7$$

$$49=7\times 7=7^2$$

Step 2: Calculate HCF.
The highest common factor is the lowest power of the common prime factor.

$$\text{HCF}(42,49)=7$$

Step 3: Calculate LCM.
The least common multiple is the product of the highest powers of all prime factors.

$$\text{LCM}(42,49)=2\times 3\times 7^2=6\times 49=294$$

Step 4: Find the ratio of LCM to HCF.

$$\text{Ratio}=\frac{\text{LCM}}{\text{HCF}}=\frac{294}{7}=\frac{42}{1}$$

Thus, the ratio is $42:1$.