75 , 189

The LCM is the smallest positive number that all of the numbers divide into evenly.

1. List the prime factors of each number.

2. Multiply each factor the greatest number of times it occurs in either number.

75 has factors of 3 and 25.

3⋅25

25 has factors of 5 and 5.

3⋅5⋅5

3⋅5⋅5

189 has factors of 3 and 63.

3⋅63

63 has factors of 3 and 21.

3⋅3⋅21

21 has factors of 3 and 7.

3⋅3⋅3⋅7

3⋅3⋅3⋅7

The LCM of 75,189 is the result of multiplying all prime factors the greatest number of times they occur in either number.

3⋅3⋅3⋅5⋅5⋅7

Multiply 3 by 3.

9⋅3⋅5⋅5⋅7

Multiply 9 by 3.

27⋅5⋅5⋅7

Multiply 27 by 5.

135⋅5⋅7

Multiply 135 by 5.

675⋅7

Multiply 675 by 7.

4725

4725

Find the LCM 75 , 189