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

Expert Answers
justaguide eNotes educator| Certified Educator

A number lying between 300 and 400 has to be determined that is divisible by 6, 8, 10 and 12. Expressed as a product of prime numbers:

6 = 3*2

8 = 2^3

10 = 2*5

12 = 2^2*3

The lowest common multiple of 6, 8, 10 and 12 is 3*8*5 = 120. The multiple of 120 that lies between 300 and 400 is 360.

The number lying between 300 and 400 that is divisible by 6, 8, 10 and 12 is 360.

mathewww | Student

In order to find the numbers divisible by 6, 8, 10 and 12 first the LCM of these numbers have to be worked out. LCM of these numbers or its multiples are divisible by them. LCM of these numbers work out to be 120. Its multiple in the range between 300 and 400 is 360. Hence, the desired number that would be divisible by 6, 8, 10 and 12 is 360. So, the final answer for a number between 300 and 400 that is divisible by 6, 8, 10 and 12 is 360.