Question

Ryan bys plates and cups for a party. There are 12 plates in a pack and 10 cups in a

pack. He wants an equal number of plates and cups for a the party. What is the least number
of packs of plates and the least number of packs of cups that Ryan must buy?

Help please

Answer 1

5 packs of plates

6 packs of cups

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Step-by-step explanation:

GCF = greatest common factor

LCM = lowest common multiple

The GCF of 12 and 10 is 2 since

• 12 = 2*6
• 10 = 2*5

It's the largest factor they have in common together.

Multiply 12 and 10, then divide by the GCF to get the LCM

LCM = (12*10)/GCF = 120/2 = 60

The LCM is 60. We can verify this by looking at a few multiples like so

• multiples of 12 are: 12, 24, 36, 48, 60, 72, ...
• multiples of 10 are: 10, 20, 30, 40, 50, 60, 70, ...

The LCM is the amount of plates and cups that match up.

Buying 5 packs of 12 plates gets 5*12 = 60 plates total

Buying 6 packs of 10 cups each gets 6*10 = 60 cups total

Answer 2

• 5 packs of plates

• 6 packs of cups

Step-by-step explanation:

5 packs of plates = 60 plates (5×12)

6 packs of cups = 60 cups (6×10)