pencils come in packages of 10. erasers come in packages of 12. Philip wants to purchase the small est number of pencils and erasers so that he will have exactly 1 eraser per pencil. how many packages of pencils and erasers should Philip buy ?
10 = 2*5
12 = 2*6
LCM(10,12) = 2*5*6 = 60
You will need 60 of each item.
This gets you the solution posted above
This question makes no sense. It's part of my sons homework. He doesn't say how many pencils he wants, just that he wants an eraser for each. So if you go off the what the question says, it should be one packages of each.
To solve this problem, we need to find the least common multiple (LCM) of the numbers 10 and 12. The LCM is the smallest number that is divisible by both 10 and 12 without leaving a remainder.
To find the LCM, we can use the prime factorization method:
Prime factorization of 10: 2 x 5
Prime factorization of 12: 2 x 2 x 3
In order to find the LCM, we take the highest power of each prime factor that appears in either prime factorization: 2^2 x 3 x 5 = 60.
Therefore, the LCM of 10 and 12 is 60.
The LCM of 10 and 12 represents the smallest number of items that Philip needs to buy to have exactly 1 eraser per pencil. As the LCM is 60, Philip should buy 60 pencils and 60 erasers.
Since each package of pencils contains 10 pencils, Philip needs to buy 60/10 = 6 packages of pencils.
Similarly, each package of erasers contains 12 erasers, so Philip needs to buy 60/12 = 5 packages of erasers.
Therefore, Philip should buy 6 packages of pencils and 5 packages of erasers to have exactly 1 eraser per pencil.