LCM for 12, 16 and 30 please help?

Question

LCM for 12, 16 and 30 please help?

Answer 1

The LCM for 12, 16 and 30 is the lowest number that'll go into them all evenly, which is 2.

Answer 2

2.

Answer 3

idk!

Answer 4

the least common multiple would be 2.

Answer 5

start by setting up multiples and seeing which number is a multiple of all those numbers:

12-

2, 6

3, 4

16-

2, 8

4, 4

30-

2, 15

3, 10

5, 6

now which number is the lowest that they all share?

Answer 6

240

12x20=240

16x15=240

30x8=240

Answer 7

the lcm is 2

Answer 8

I'm not sure this question needs another answer but here goes.  This process can be applied to any group of numbers.

We have a theorem that says that for any integers a and b:

lcm(a,b) = (ab)/gcd(a,b)

Where we obtain the gcd(a,b) by the Euclidean Algorithm.

The lcm(12,16,30) is equivalent to lcm(lcm(12,16),30).

Thus we first compute lcm(12,16):

By our theorem lcm(12,16) = (12)(16)/gcd(12,16)

By the Eucldiean Algorithm gcd(12,16) = 4 , since

16 = 1*12 + 4

12 = 3*4 + 0

Thus lcm(12,16) = (12)(16)/(4) = 48

Now we compute lcm(48,30)

lcm(48,30) = (48)(30)/gcd(48,30)

By the Euclidean algorithm gcd(48,30) = 6 , since

48 = 1*30 + 18

30 = 1*18 + 12

18 = 1*12 + 6

12 = 2*6 + 0

Thus lcm(12,16,30) = lcm(48,30) = (48)(30)/(6) = 240

Answer 9

To find LCM and GCD, use the prime factors:

12 = 2*2*3

16 = 2*2*2*2

30 = 2*3*5

The smallest number that can be divided by all of them must contain as many primes as each one:

We need four 2's (this covers all of them, including the 16), we need one three (to cover the 12 and 30) and we need one five:

2*2*2*2*3*5 = 240

No smaller number can do, because any smaller number would be missing one fo the required factors.

To find the biggest number that can divide all three, we can only take factors that are common to all of them:

That is 2.

We cannot take a 3 (no 3 in 16) and we cannot take a 5 (no 5 in 12).  We cannot take another 2 (there is only one 2 in 30)

Answer 10

12 = 2*2*3

16 = 2*2*2*2

30 = 2*3*5

The LCM will then need 4 2's, one 3 and one 5

2*2*2*2*3*5 = 240

Answer 11

beats me!

Answer 12

2

Answer 13

2, I think.  Ive been out of school for over ten years.

Answer 14

To find the LCM, start by factoring each number:

12 = 2*2*3

16 = 2*2*2*2

30 = 2*3*5

Then, for each factor, see where it appears the most.  For example, 2 appears twice in the factors for 12, four times in the factors of 16, and once in the factors for 30.  Then multiply each factor together the highest number of times that it appears.

2*2*2*2*3*5 = 240