Big Ideas Math: Modeling Real Life, Grade 6
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5. Least Common Multiple
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Exercise 9 Page 29

Use the factor pairs of

Example Solution: and

Practice makes perfect

The least common multiple (LCM) of two numbers is the smallest whole number that is a multiple of both numbers. Let's see a few examples!

Numbers Multiples of Numbers Common Multiples Least Common Multiple
and
and
We want to find three numbers that have a least common multiple of To do so, recall that a factor pair is a combination of two factors that can be multiplied together to equal a number. Let's find the factor pairs of by listing its factors!
Now, we can write the factor pairs of each number by finding the product of two factors that equals
Number Product of Two Factors Factor Pairs

Remember that when a number is multiplied by an integer, the result is a multiple of the first number.

Note that the above products have the same form as the products we used to find the factor pairs. Then, we can list these products to identify the numbers that have as a multiple. Let's do it!
Now we can list the multiples of the numbers that have as a factor to find three numbers with an LCM equal to Let's ignore the and because they are the identities.
From the above list, we can see that and have an LCM of Note that there are other three-number sets we could create out of this list that have an LCM of