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

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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

12:2x2x3

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

lcm=2x2x2x3x5=120

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

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The number we seek is 360

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