Using Divisibility Cheat Codes to Find Multiples
RECALL
• A multiple of a number is the product of that number times another whole
number that is greater than 0.
e.g. Multiples of 5 could be: 5 x 1 = 5; 5 x 2 = 10; 5 x 3 = 15; etc.
• Common multiples are those shared by more than one number.
eg.
Some of the multiples of 2 are: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20
Some of the multiples of 4 are: 4, 8, 12, 16, 20, 24
The common multiples of 2 & 4 are: 4, 8, 12, 16, 20
• The Lowest Common Multiple (LCM) is the smallest multiple that is common
to each of a series of numbers.
e.g. Find the LCM of 15 and 10:
The multiples of 15 are: 15, 30, 45, 60, 75, 80, 95...
The multiples of 10 are: 10, 20, 30, 40, 50, 60, 70, 80...
30, 60, 80... are all common multiples of 10 & 15, but 30 is the lowest
multiple common to both numbers (LCM)
THINK
Is 2 a multiple of 1340? How do you know?
Is 3? How do you know?
Is 4? How do you know?
Is 5? How do you know?
Is 6? How do you know?
Is 8? How do you know?
Is 9? How do you know?
Is 10? How do you know?
Using Divisibility Cheat Codes to Find Multiples – Exercise
1) a) List the multiples of each number, up to 100.
a) 4
b) 5
c) 7
d) 8
e) 9
b) What pattern do you notice about the number of multiples in each row? Why do you
think this is happening?
2) a) List the common multiples of 4 & 8 up to 100. Circle the LCM.
b) List the common multiples of 5 & 7 up to 100. Circle the LCM.
c) List the common multiples of 4 & 9 up to 100. Circle the LCM.
3) Indicate the multiples of each of the following numbers by writing “M” for multiple in
the appropriate box.
2
1135
2187
6450
3274
9364
3
4
5
6
8
9
10
4) A candle factory needs to ship an order of 184 scented candles. The factory will ship the
candles in several boxes. Each box must contain the same number of candles. How many boxes
could the factory use for the order: 4, 5, 6, or 10? How do you know?
5) Roopa is organizing 850 blocks into bins at the toy store. She needs to put the same number of
blocks in each bin without any leftover blocks. How many bins could Roopa use for the blocks: 6,
10, 9, or 3? How do you know?
6) Dave bought a big bag of candy at a warehouse store. There are 951 pieces of candy in the bag.
Dave needs to divide the candy up into smaller bags. He wants to put the same number of pieces
in each small bag. How many small bags could Dave use: 3, 9, 5, or 4?
7) A muffin factory made 3,656 blueberry muffins. After arranging the muffins into packages, the
factory did not have any leftover muffins. How many muffins could the factory be putting in
each package: 5, 2, 10, or 6?