The ratio of the LCM of two numbers to the sum of the same two numbers is 12 : 7. If their HCF is 4, what is the product of these two numbers?

HCF of two numbers is 4.

So let's assume the two numbers are '4a' and '4b'.

So the LCM of '4a' and '4b' is '4ab'.

The ratio of the LCM of two numbers to the sum of the same two numbers is 12 : 7.

$$\frac{4ab}{4a+4b}\ =\ \frac{12}{7}$$

$$\frac{ab}{a+b}\ =\ \frac{12}{7}$$

As per the above-given equation, the product of 'a' and 'b' should be 12 and their sum is 7.

So the values of 'a' and 'b' will be 4 and 3.

two numbers = 4a and 4b

= $$4\times4$$ and $$4\times3$$

= 16 and 12

product of these two numbers = $$16\times12$$

= 192