A factory is to pack pencils in boxes of 8 and 10 pieces. What is the smallest number of pencils that can be packed using the boxes.*
Prime factors of 8:
8 = 2 ∙ 2 ∙ 2
Primes factors of 10:
10 = 5 ∙ 2
If you multiply them all together:
2 ∙ 2 ∙ 2 ∙ 5 ∙ 2 = 8 ∙ 10 = 80.
80 is the smallest number of pencils that can be packed using the boxes.
a. smallest number of pencils that can be packed
b. pack pencils in boxes of 8 and 10 pieces
c. LCM
d. 8: 8,26,24,32,”40”,48,56
10: 10,20,30,”40”,50,60
e.40 is the smallest number of pencils that can be packed using the boxes
LCM(8,10) = 40
To find the smallest number of pencils that can be packed using boxes of 8 and 10 pieces, we need to find the least common multiple (LCM) of 8 and 10.
The LCM is the smallest multiple that two or more numbers have in common.
One way to find the LCM is by listing the multiples of each number and finding the first multiple they have in common.
Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, ...
Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, ...
From the lists above, we can see that the first multiple they have in common is 40. Therefore, 40 is the smallest number of pencils that can be packed using boxes of 8 and 10 pieces.