It is known that the greatest common divisor of a and b is 10, and the least common multiple of a and c, b and c is 90. Then, how many groups of natural numbers a, b, c satisfy the above conditions.
已知a与b的最大公约数是10，a与c、b与c的最小公倍数都是90．那么，满足以上条件的自然数a、b、c有多少组．
<gadget id="calculator">5 * 4</gadget>
<output>20</output>

<result>20</result>