Grade 6

Review: GCF and LCM

Ideas

Review: GCF and LCM

Review: GCF and LCM

Let's differentiate between GCF and LCM.

The GCF, or Greatest Common Factor, is the largest number that divides evenly into each number in a given set of numbers. Finding the GCF may start with finding the factors of the given pair or set of numbers. Factors are numbers that divide the given number completely without leaving a remainder.

The LCM, or Least Common Multiple, is the smallest positive multiple that is common to two or more numbers. Finding the LCM may start with finding the first few multiples of each of these numbers. Multiples are products obtained by multiplying a number with another number.

We need to pay attention to key words in the question to know which number we need to find.

Examples

Example 1

Consider the numbers: 6,\,10,\,12.

Find the GCF.

Worked Solution

Create a strategy

We list the factors of the set of numbers. We then choose the greatest common number among all the factors in the set.

Apply the idea

By listing the factors, we have:

6:\,1,\,2,\,3,\, 6
10:\,1,\,2,\,5,\, 10
12:\,1,\,2,\,3,\, 4,\,6,\,12

There is only one common factor which is also the greatest common factor of 6,\,10\, and 12, 2. Therefore the GCF is 2.

Find the LCM.

Worked Solution

Create a strategy

We can start by considering the first 10 multiples of 6,\,10 and 12, and choose the smallest number that appears in each of the lists. If it does not appear, we will have to find more multiples.

Apply the idea

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,\,90,\,100

The multiples of 12 are: 12,\,24,\,36,\,48,\,60,\,72,\,84,\,96,\,108,\,120

The least common multiple of 6,\,10 and 12 is 60.

Idea summary

The Greatest Common Factor or GCF is the largest number that divides evenly into each number in a given set of numbers.

The Least Common Multiple or LCM is the smallest positive multiple that is common to two or more numbers.

Outcomes

6.NS.B.4

Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor.

Review: GCF and LCM

Ideas