Prime factor each number and line like factors up in columns
60 = 2^2 * 3 * 5
100 = 2^2 * 5^2
75 = 3 * 5^2
120= 2^3 * 3 * 5
From each column, take the factor with the largest power and multiply these together......so we have :
2^3 * 3 * 5^2 =
8 * 3 * 25 =
24 * 25 =
600
And that's the LCD