Eggs come in packages of 12 and English muffins come in packages of 10. What is the least number of
packages of each that can be bought to be able to make egg sandwiches with no muffins or eggs left
over?
5 packs of eggs or 6 packs of buns.
Hope this helps!
THX
To determine the least number of packages of eggs and English muffins needed to make egg sandwiches without any leftovers, we need to find the least common multiple (LCM) of 12 and 10.
First, let's find the LCM of 12 and 10.
12 = 2^2 * 3
10 = 2 * 5
The LCM is the product of the highest powers of all prime factors in both numbers. Thus, the LCM of 12 and 10 is:
LCM(12, 10) = 2^2 * 3 * 5 = 60
So, to make egg sandwiches without any leftovers, you would need to buy 60 English muffins (in packages of 10) and 60 eggs (in packages of 12).
To find the least number of packages of eggs and English muffins needed to make egg sandwiches with no leftovers, we can use a method called "least common multiple" (LCM).
The LCM is the smallest multiple that two or more numbers have in common. In this case, we need to find the LCM of 12 (number of eggs per package) and 10 (number of English muffins per package).
To find the LCM, we can start by listing the multiples of each number until we find a common multiple:
Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120...
Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120...
From the lists above, we see that the first common multiple of 12 and 10 is 60.
Therefore, the least number of packages of each that can be bought to make egg sandwiches with no leftovers is 60 eggs (5 packages of 12) and 60 English muffins (6 packages of 10).