Question 313391
Look at first digits. 
100 series numbers are out since 199 gives the largest product=81<120.
200 series numbers are also out since no two digits multiplied together produce 60. 
300 series numbers remaining digits need a product of 40: 358,385
400 series numbers remaining digits need a product of 30: 456,465
500 series numbers remaining digits need a product of 24: 524,538,542,583
600 series numbers remaining digits need a product of 20: 545,554
700,800,900 series numbers are out since 7,8,and 9 do not evenly divide 120.
Counting them up gives 10 3 digit numbers. 
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EDIT
Oops!
800 series numbers remaining digits need a product of 15: 835, 853
That adds 2. 
SO there are {{{highlight_green(12)}}} 3 digit numbers that whose product is 120.