# Math training: divisibility of natural numbers, gcd, LCM

Divisibility rule gcd (6,9) LCM (6,8)

Score: Level: Error: Time:

Answer   ### Divisibility rules for numbers

2: The last digit is even (0, 2, 4, 6, or 8).
3: Sum the digits. The result must be divisible by 3.
5: The last digit is 0 or 5.
9: Sum the digits. The result must be divisible by 9.
10: The ones digit is 0.

### What is the LCM of 4 and 6?

Multiples of 4 are:
4, 8, 12, 16, 20, 24, 28, 32, ...
and the multiples of 6 are:
6, 12, 18, 24, 30, 36, ...
Common multiples of 4 and 6 are simply the numbers that are in both lists:
12, 24, 36, 48, 60, 72, ....
So, from this list of the first few common multiples of the numbers 4 and 6, their least common multiple is 12.

### What is the greatest common divisor of 54 and 24?

Thus the divisors of 54 are: 1 , 2 , 3 , 6 , 9 , 18 , 27 , 54.
Similarly, the divisors of 24 are: 1 , 2 , 3 , 4 , 6 , 8 , 12 , 24.
The numbers that these two lists share in common are the common divisors of 54 and 24:
1 , 2 , 3 , 6.
The greatest of these is 6. That is, the greatest common divisor of 54 and 24.
One writes: gcd ( 54 , 24 ) = 6.

Victory

Congratulations, you win 