saisumanth
saisumanth saisumanth
  • 14-05-2022
  • Mathematics
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a natural number when divided by 12 15 18

a natural number when divided by 12 15 18 class=

Respuesta :

dariusjonathanteng35 dariusjonathanteng35
  • 14-05-2022

Answer:

173

Step-by-step explanation:

Assume the natural number is x.

x/12 = ... R 5

x/15 = ... R 8

x/18 = ... R 11

Thus, x+7 is divisible by 12, 15 and 18 all together.

The smallest possible number of x+7 can be calculated with prime factorization.

12=2^2 * 3

15=3 * 5

18=2 * 3^2

The smallest possible number for x+7 is 2^2 * 3^2 * 5 = 4 * 9 * 5 = 180.

Therefore, the smallest possible solution for x is 180 - 7 = 173.

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