Lcm of two natural number a and b is 300 .how many such pairs of a and b exists

300 = 3 * 100 = 2^2 * 3 * 5^2

So, one of the two numbers should have 2^2 as a factor, the other number can have 2^0 or 2^1 or 2^2 as a factor.
Similarly, one of the two numbers should have 3^1 as a factor and the other number can have 3^0 or 3^1 as a factor.
One of the two numbers should have 5^2 as a factor and the other number can have 5^0 or 5^1 or 5^2 as a factor.
The number of ways in which the number having the factor 2^2 can be selected is 2. The other number can have one of the three factors. So, 2*3 = 6 ways There is one repetition. So, number of possibilities = 6-1 = 5 ways
Similarly, for 5, it is 5 ways and for 3, it is 2*2 = 4. Number of ways without repetition = 3 ways
So, the number of possible pairs of numbers is 5*5*3 = 75

If H=(x^a)*(y^b)*(z^c) no of pairs with lcm=H=(2a+1)*(2b+1)*(2c+1)/2
Here ans=5*5*3+1/2=38

Ans is 38..

Bro answer is wrong answer should be 38 as given in my book. Pls give me a other solution