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

Answer:

$a * b = 210^4$

Step-by-step 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 $210^4$