Write each number in factored form:
39 = 3 x 13
9 = 3 x 3
117 = 3 x 39 = 3 x 3 x 13
Take each factor the greatest number of times in each number; 3 x 3 x 13 = 117.
Each number, 13, 3, and 117 will divide into 117 without a remaider (and, no smaller number will work) ; therefore, it is the least common multiple.
39=3*13
117=3*3*13=3*39
so 117 is a multiple of 39
9=3*3 so 117 is a multiple of 9
so the lowest common multiple is 117