contestada

Produce the least positive number that is divisible by​ 2, 3,​ 4, 5,​ 6, 7,​ 8, 9,​ 10, and 11.

Respuesta :

because all numbers that are divisible by 10 is divisible by 5, all numbers that are divisible by 8 is divisible by 2 and 4, all numbers divisible by 6 is divisible by 2 and 3, we only need to find the smallest common multiple of 6,7,8,9,10 and 11
find the prime factors of each:
2,3
7
2,2,2,
3,3,
2,5,
11
factors that are shared can be used only once, so we have:
2*7*3*11*3*2*5*2=27720
facundo3141592

We want to get the least positive number that is divisible by 2, 3,​ 4, 5,​ 6, 7,​ 8, 9,​ 10, and 11. The number is 27,720

Remember that any number N can be written as a product of prime factors, so to get the minimum number divisible by all the given factors, we need to see which primes we need to make it.

we have:

  • the factor 2.
  • the factor 3.
  • the factor 4 = 2*2  (we already had a factor 2, so we just add another)
  • the factor 5
  • the factor 6 = 2*3  (notice that we already have a two and a 3, so we already have this factor).
  • the factor 7
  • the factor 8 = 2*2*2 (so we add another factor 2)
  • the factor 9 = 3*3 (so we add another 3)
  • the factor  10 = 2*5 (we already have this)
  • the factor 11

Then the number is:

N = (2*2*2)*(3*3)*5*7*11

Notice that any of the given numbers can be made with these factors, by solving the multiplication, we have:

N = 27,720

If you want to learn more about multiples and factors, you can read:

https://brainly.com/question/1089338

Otras preguntas