Find the number of ordered pairs of positive integers (a,b)(a, b)(a,b) such that lcm(a,b)=10!\text{lcm}(a, b) = 10!lcm(a,b)=10! and gcd(a,b)=1\text{gcd}(a, b) = 1gcd(a,b)=1.
2102^{10}210
282^828
272^727
292^929