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paula and ricardo are serving cupcakes at a school party. if they arrange the cupcakes in groups of 2,3,4,5 or 6, they always have exactly one cupcake leftover. what is the smallest number of cupcakes they could have?

Respuesta :

mathstudent55
Find the smallest number that is divisible by 2, 3, 4, 5, 6 and add 1.
We need the least common multiple of 2, 3, 4, 5, 6.

2 = 2
3 = 3
4 = 2^2
5 = 5
6 = 2 * 3

LCM = product of common and not common prime factors with larger exponent.

LCM = 2^2 * 3 * 5 = 4 * 3 * 5 = 60

To always have a remainder of 1, you need of add 1 to 60.

The number is 61.

Check:
61/2 = 30 remainder 1
61/3 = 20 remainder 1
61/4 = 15 remainder 1
61/5 = 12 remainder 1
61/6 = 10 remainder 1
MrRoyal

The smallest number of cupcakes is an illustration of LCM

The smallest number of cupcakes is 61

The groups are given as:

[tex]\mathbf{Group = 2, 3,4,5,6}[/tex]

The remainder is given as:

[tex]\mathbf{Remainder = 1}[/tex]

First, we calculate the LCM of 2 to 6

Write out the factors

[tex]\mathbf{2 = 1 \times 2}[/tex]

[tex]\mathbf{3 = 1 \times 3}[/tex]

[tex]\mathbf{4 = 1 \times 2 \times 2}[/tex]

[tex]\mathbf{5 = 1 \times 5}[/tex]

[tex]\mathbf{6 = 1 \times 2 \times 3}[/tex]

So, the LCM is:

[tex]\mathbf{LCM = 1 \times 2 \times 2 \times 3 \times 5}[/tex]

[tex]\mathbf{LCM = 60}[/tex]

Add the remainder, to get the smallest number of cupcakes

[tex]\mathbf{Smallest =LCM + Remainder}[/tex]

[tex]\mathbf{Smallest =60 + 1}[/tex]

[tex]\mathbf{Smallest =61}[/tex]

Hence, the smallest number of cupcakes is 61

Read more about LCMs at:

https://brainly.com/question/3000263

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