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Annmarie is making a mosaic wall hanging. Large tiles come in packages of 5. Medium tiles come in packages of 8. Small tiles come in packages of 12. Annmarie wants to use the same number of large, medium, and small tiles in her wall hanging. What is the least number of tiles she could use?

Respuesta :

roohafzah

Answer :

  • 120 tiles

Explanation :

break down the numbers into prime factors

  • 5 = 1 x 5
  • 8 = 1 x 2 x 2 x 2
  • 12 = 1 x 2 x 2 x 3

now, multiply the highest degree of each factor together

  • 5^1 x 2^3 x 3^1
  • 5 x 8 x 3
  • 120

thus, Marie would need a least of 120 tiles ( 120/5 = 24 packages of large tiles , 120/8 = 15 packages of medium tiles and 120/12 = 10 packages of small tiles ) .

msm555

Answer:

120 tiles

Step-by-step explanation:

To find the least number of tiles Annmarie could use, we need to find the least common multiple (LCM) of the quantities of tiles in each package.

The quantities are:

  • Large tiles: 5 tiles per package
  • Medium tiles: 8 tiles per package
  • Small tiles: 12 tiles per package

The LCM of these numbers will give us the smallest number of tiles that is divisible by all three quantities.

The prime factorization of these numbers is:

[tex]5 = 5[/tex]

[tex]8 = 2^3[/tex]

[tex]12 = 2^2 \times 3[/tex]

To find the LCM, we take the highest power of each prime factor that appears in any of the numbers:

The LCM will contain [tex]5[/tex], [tex]2^3[/tex], and [tex]3[/tex].

So, the LCM is [tex]5 \times 2^3 \times 3 = 5 \times 8 \times 3 = 120[/tex].

Therefore, Annmarie would need at least 120 tiles in total.

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