Find the number lying between 300 and 400 which is divisible by 6,8,10,12.

Expert Answers
embizze eNotes educator| Certified Educator

Find the number between 300 and 400 that is divisible by 6,8,10, and 12.

Since the number we seek is divisible by 6,8,10,and 12 it will be divisible by their least common multiple. (The least common multiple, lsm, is the smallest number that the given numbers are factors of.)

To find the lcm by hand we could list all multiples of each number and find the lowest such multiple. Another way is to list the factors of each, and realize that the lcm has each factor:

6: 2x3

8: 2x2x2

10: 2x5


The lcm will have as a factor each factor that appears, and to its highest degree:


The smallest multiple of 120 that is between 300 and 400 is 360.


The number we seek is 360


oldnick | Student

Fisrst yoyu ave to see that a number divisible by 6,8,10,12 is divisible by  low. common multyplers of them.


So common multiply of 6,8,10,12 is 360