10 , 18 , 36

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.

10 has factors of 2 and 5.

2⋅5

18 has factors of 2 and 9.

2⋅9

9 has factors of 3 and 3.

2⋅3⋅3

2⋅3⋅3

36 has factors of 2 and 18.

2⋅18

18 has factors of 2 and 9.

2⋅2⋅9

9 has factors of 3 and 3.

2⋅2⋅3⋅3

2⋅2⋅3⋅3

The LCM of 10,18,36 is the result of multiplying all prime factors the greatest number of times they occur in either number.

2⋅2⋅3⋅3⋅5

Multiply 2 by 2.

4⋅3⋅3⋅5

Multiply 4 by 3.

12⋅3⋅5

Multiply 12 by 3.

36⋅5

Multiply 36 by 5.

180

180

Find the LCM 10 , 18 , 36