 # Greatest Common Factor and Least Common Multiples GCF and LCM

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Greatest Common Factor and Least Common Multiples GCF and LCM

What is the difference between a factor and a multiple?

Give me an example of a factor of 15

Give me an example of a multiple of 15

How would you find the GCF of 60 and 96?

There are actually 3 ways
There are actually 3 ways. You can use prime factorization, write out all the prime factors for each number or extract common prime numbers.

List the factors of 60: 1,2,3,4,5,6,10,12,15,20,30,60 List the factors of 96 1,2,3,4,6,8,12,16,24,32,48,96 find the largest factor - 12

…or do prime factorization
…or do prime factorization. Circle all the primes the 2 numbers have in common and multiply one set of them to get your GCF. 96 60 48 2 2 30 24 2 15 2 12 2 3 5 6 2 2 x 2 x 3 = 12 2 3

This, to me, is the easiest way. Try it!
…or you can extract the common prime factors of 60 and 96 and form a product to give the GCF. This, to me, is the easiest way. Try it! 2 60, 96 2 x 2 x 3 = 12 2 30, 48 3 15, 24 5, 8

Find the GCF (HCF) of 36, 24, 144 and 96

96 24 36 48 2 2 12 18 2 24 2 6 9 2 2 12 2 3 2 3 3 6 2 144 2 3 12 12 3 4 2 x 2 x 3 = 12 3 4 2 2 2 2

2 36, 24, 144, 96 2 x 2 x 3 = 12 2 18, 12, 72, 48 3 9, 6, 36, 24 3 2 12 8

There are 3 ways to find the LCM as well
There are 3 ways to find the LCM as well. You can list the multiples of the numbers, do prime factorization, or extract the prime factors from either one or both numbers. Find the LCM of 12 and 18

Multiples of 12 are… 12,24,36,48,60,72,…. Multiples of 18 are… 18,36,54,72,90,108,… The smallest multiple the 2 numbers have in common is the least common multiple.

…or do prime factorization
…or do prime factorization. Write down the number they have in common only once, then write down the leftover numbers. Multiply them all together. 12 18 9 4 2 3 3 3 2 2 Numbers in common are 2 and 3 Leftover numbers are 2 and 3 2 x 3 x 2 x 3 = 36

Remember…the numbers you pull out have to be prime numbers!
2 12, 18 2 6, 9 3 3, 9 3 1, 3 1 1 2 x 2 x 3 x 3 = 36

Find the LCM of 35, 420 and 245

245 35 420 42 5 49 10 5 7 5 7 7 2 6 7 2 3 Numbers they have in common: 5 and 7 Leftover numbers: 2, 3, 2, 7 Multiply them all together: 5 x 7 x 2 x 3 x 2 x 7 = 2940

primes 5 35, 420, 245 7 7, 84, 49 7 1, 12, 7 3 1, 12, 1 2 1, 4, 1 2 1, 2, 1 1, 1, 1 5 x 7 x 7 x 3 x 2 x 2 = 2940

Find the GCF and LCM of 28 and 63

GCF = 7 LCM = 7 x 4 x 9 = 252

Find the GCF and LCM of 12 and 13

GCF = 1 LCM = 1 x 12 x 13 = 156

Find the GCF and LCM of 27, 21, 33 and 15

GCF = 3 LCM = 3 x 9 x 7 x 11 x 5 = 10,395

Start tonight’s homework. No calculators!

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