LCM of 2, 3, 4, 5 (perfect square, cube, 4th and 5th power) is 60. That will be the exponent for each of your prime factors, 2 3 and 5 . So your smallest integer is (2^60)x(3^60)x(5^60), which can be written as 30^60. Making a=30 and b=60. So a+b = 90. The divisibility by 4 condition is taken care of with 2^60, so you…