find the least common multiple (LCM) for each of the following group of number?

Question

Find the least common multiple (LCM) for each of the following groups of number. Use which ever method you wish. 12, 20, and35

Answer 1

420 = 12 (35)
420 = 21 (20)
420 = 35 (12)
You can't divide these numbers (12, 21, 35) to find anything lower that is all divisible by the same number.

LCM = 420

Answer 2

You find the LCM's by breaking numbers down into their prime factors, and then seeing the MINIMUM set of those prime factors which will contain enough primes to satisfy what are individually in each of the initial numbers. (Don't worry, this may sound like gobbledygook, but the examples should make this plain!) 1. 16 = 2^4 and 12 = 3 (2^2). So the LCM has to have 4 "2's" in it (from the 16). The 12's two "2's" are therefore taken care of, but the LCM has to have an additional number, a ' 3 ' in it, for it to be divisible by 12. So the LCM has a " 3 " and four " 2's " in it, so it's 3 x 16 = 48. CHECK: Sure enough, 48 = 3 x 16 and 4 x 12. There's no lower multiple of either 12 or 16 which would be divisible by the other. 2. 12 = 3 (2^2) and 8 = 2^3. So this time the LCM will need 3 " 2's " (from the 8) and a " 3 " (from the 12). Once again,the 12's "2's" are already accounted for. So the LCM = 3 x 8 = 24. (Again, you can see for yourself that no lower number will do.) I really don't understand why the second part is distinguished by a different kind of instruction. It's the same kind of problem, and it's solved in the same way. The only thing is that the use of the term "for each group of numbers" suggests to me that there should be MORE than a PAIR in them (as was the case for the first two problems). Is there some confusion about the question because you don't have access to the original problem sheet? In any case, you said you could help your daughter with the rest, so I'm taking you at your word. Good luck! Live long and prosper. Postscripts 1. I'll leave you to show why, but in the second set, the answers should be: 1.) 450 and 2.) 286. See if you can confirm these. 2 I'm a retired astrophysicist. I second what the retired mathematics teacher says, below. Good for you for wanting to understand this and help your daughter.

Answer 3

420

The multiples of 12 that end in 0 are multiples of 60.
The multiples of 35 that end in 0 are multiples of 70.
Find the LCM of 60 and 70-420. 420 is also a multiple of 20.

Or you can simply multiply 35 by 12 to get 420.

Here's another way: find the factorization of each number and then multiply the distinct factors.

12= 4 * 3
20 = 4 * 5
35 = 7 *5
4 *3*5*7 = 420

Answer 4

12 = 2^2 * 3
20 = 2^2 * 5
35 = 5 * 7
for LCM, all numbers with the greatest exponent.
LCM: 12 U 20 U 35 = 2^2 * 3 * 5 * 7 = 420

**also, for GCF, common numbers with the least exponent.

Answer 5

12 = 4*3
20 = 4*5
35 = 5 *7
So LCM is 7*5*4*3= 420

Answer 6

12*35=420

Answer 7

6 and 8=48

Answer 8

Do your own homework. How do you expect to learn anything? You should be ashamed! I am a former teacher who could tell you the answer but won't. Here is a hint though

12, 24,.....
20, 40....
35,70.....Just keep writing multiples(use a calculator) until you find a common one. There is a faster way, but this way will work and is easy to remember.

Answer 9

Use factor trees. These don't have a common multiple smaller than themselves. 420 is their common multiple.

3x2x2,2x2x5,5x7...4x3x5x7=420

Answer 10

12=2*2*3
20=2*2*5
35=5*7
LCM=2*2*3*5*7=420