Answer:

1. 300

2. 90

3.120

Step-by-step explanation:

1.

Find the prime factors of 15

       15

   /    \

      3      5

Find the prime factors of 100:

      100

   /   \

     2      50

        /  \

           2    25

        /  \  

            5    5

The least common multiple is the product of all factors in the greatest number of their occurrence.

LCM = 2x2x3x5x5

LCM = x 3 x 5

LCM = 300

The least common multiple of 15 and 100 is 300.

2.

find the prime factors of 18

      18

   /  \

    2     9    

     /   \

     3         3

Find the prime factors of 30:

         30

    /    \

     2         15

          /  \

              3        5

The least common multiple is the product of all factors in the greatest number of their occurrence.

LCM = 2x3x3x5

LCM = 2x3x3

LCM = 90

The least common multiple of 18 and 30 is 90.

3.

Find the prime factors of 30

     30

  /   \

  2       15

      /  \

        3      5

Find the prime factors of 40

       40

   /   \

  2         20

        /  \

           2      10

            / \

                 2      5

The least common multiple is the product of all factors in the greatest number of their occurrence.

LCM = 2x2x2x3x5

LCM = 2x3x5

LCM = 120

The least common multiple of 30 and 40 is 120.