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Illustrative Math
Grade 6
Let’s use multiples to solve problems.
Illustrative Math Unit 6.7, Lesson 17 (printable worksheets)
The following diagram explains what is a common multiple and how to find the least common multiple of two whole numbers.
Circle all the multiples of 4 in this list.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
Circle all the multiples of 6 in this list.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
What do you notice? What do you wonder?
Scroll down the page for the solutions to the “Are you ready for more?” section.
A florist can order roses in bunches of 12 and lilies in bunches of 8. Last month she ordered the same number of roses and lilies.
The least common multiple of 6 and 8 is 24.
20
12
If one number is a multiple of the other then the least common multiple is the larger number.
If we list out the multiples of the numbers, we will find that the larger number is the least common multiple because it is a multiple of the smaller number.
Lin’s uncle is opening a bakery. On the bakery’s grand opening day, he plans to give away prizes to the first 50 customers that enter the shop. Every fifth customer will get a free bagel. Every ninth customer will get a free blueberry muffin. Every 12th customer will get a free slice of carrot cake.
common multiple
A common multiple of two numbers is a product you can get by multiplying each of the two numbers by some whole number. For example, 30 is a common multiple of 3 and 5, because 3 · 10 = 30 and 5 · 6 = 30. Both of the factors, 10 and 6, are whole numbers.
The multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33 . . .
The multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40 . . .
The common multiples of 3 and 5 are 15, 30, 45, 60 . . .
least common multiple
The least common multiple of two numbers is the smallest product you can get by multiplying each of the two numbers by some whole number. Sometimes we call this the LCM. For example, 30 is the least common multiple of 6 and 10.
The multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, 54, 60 . . .
The multiples of 10 are 10, 20, 30, 40, 50, 60, 70, 80 . . .
The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.
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