Question

If $a$ and $b$ are positive integers such that $\gcd(a,b)=210$, $\mathop{\text{lcm}}[a,b]=210^3$, and $a

Answer 1

`a * b = 210^4`

Explanation:

Given

`a,b>0`

`gcd(a,b) = 210`

`lcm(a,b) = 210^3`

Required

The product of a and b --- missing from the question

To do this, we make use of the following formula:

`a * b = gcd(a, b) * lcm(a, b)`

So, we have:

`a * b = 210 * 210^3`

Using the product law of indices, we have:

`a * b = 210^4`

This means that the product of a and b gives
`210^4`