Let a and b be positive integers. Then ab = gcd(a, b)∙lcm(a, b).
Please prove it and show the intermediate steps . [Hint: Use the prime factorizations of a and b and the formulae for gcd(a, b) and lcm(a, b) in terms of these factorizations.]
Verify that gcd(768, 576)∙lcm (768, 576) = 768*576 .