It is known that the greatest common divisor of a and b is 4, the least common multiple of a and c, b and c is 100, and a≤b. How many groups of natural numbers a, b, and c satisfying the conditions are there?
已知a与b的最大公约数是4，a与c、b与c的最小公倍数都是100，而且a≤b．满足条件的自然数a、b、c共有多少组？
<gadget id="calculator">3 * 3</gadget>
<output>9</output>

<result>9</result>