Method 1 List all the factors of each number.

Factors of  24 1 ,   2 ,   3 ,   4 ,   6 ,   8 ,   12 ,   24 Find the common factors :   1 ,   2 ,   4 ,   8. Factors of  64 1 ,   2 ,   4 ,   8 ,   16 ,   32 ,   64 The greatest common factor is  8. table with 2 rows and 3 columns , row1 column 1 , cap factorsof . 24 , column 2 1 comma 2 comma 3 comma 4 comma 6 comma 8 comma 12 comma 24 , column 3 cap findthecommonfactors . colon 1 comma 2 comma 4 comma 8. , row2 column 1 , cap factorsof . 64 , column 2 1 comma 2 comma 4 comma 8 comma 16 comma 32 comma 64 , column 3 cap thegreatestcommonfactoris . 8. , end table

The GCF of 24 and 64 is 8.

Method 2 Use the prime factorization of each number.

24 = 2 ⋅ 2 ⋅ 2 ⋅ 3 Find the prime factorization of each number . 64 = 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2   GCF = 2 ⋅ 2 ⋅ 2 = 8 The product of the common prime factors is the GCF . table with 3 rows and 2 columns , row1 column 1 , 24 equals 2 dot 2 dot 2 dot 3 , column 2 cap findtheprimefactorizationofeachnumber . . , row2 column 1 , 64 equals 2 dot 2 dot 2 dot 2 dot 2 dot 2 , column 2 , row3 column 1 ,

Method 1 List the multiples of each number.

Multiples of  12 Multiples of  18 12 ,   24 ,   36 ,   … 18 ,   36 ,   … List the multiples of each number until you find the first common multiple . table with 1 row and 3 columns , row1 column 1 , table with 2 rows and 1 column , row1 column 1 , cap multiplesof . 12 , row2 column 1 , cap multiplesof . 18 , end table , column 2 table with 2 rows and 1 column , row1 column 1 , 12 comma 24 comma 36 comma dot dot dot , row2 column 1 , 18 comma 36 comma dot dot dot , end table , column 3 table with 2 rows and 1 column , row1 column 1 , cap listthemultiplesofeachnumberuntilyoufind , row2 column 1 , thefirstcommonmultiple . . , end table , end table

The LCM of 12 and 18 is 36.

Method 2 Use the prime factorization of each number.

12 = 2 ⋅ 2 ⋅ 3   18 = 2 ⋅ 3 ⋅ 3   LCM = 2 ⋅ 2 ⋅ 3 ⋅ 3 = 36 Use each prime factor the greatest number of times it appears in either number . table with 3 rows and 2 columns , row1 column 1 , 12 equals 2 dot 2 dot 3 , column 2 , row2 column 1 , 18 equals 2 dot 3 dot 3 , column 2 , row3 column 1 ,