Greatest Common Divisor and Least Common Multiple

The greatest common divisor of a collection of integers is the largest integer that evenly divides every integer in the collection.

To find the greatest common divisor of a collection of integers,

$\blacktriangleright$ Evaluate

gcd(35, 15, 65) =  5

gcd$\left(\vphantom{ 910,2405,5850,2665}\right.$910, 2405, 5850, 2665$\left.\vphantom{ 910,2405,5850,2665}\right)$ =  65

gcd$\left(\vphantom{ 104,221}\right.$104, 221$\left.\vphantom{ 104,221}\right)$ =  13

Note    If you enter the function gcd from the keyboard while in mathematics mode, the gc appears in red italics until you type the d, then the function name gcd changes to a gray, nonitalic gcd. Scientific Notebook substitutes the function gcd for the three-letter sequence g, c, and d. You can also choose gcd from the dialog that appears when you click itbpF0.2992in0.3001in0.0692infunction.wmf or choose Insert + Math Name.

The least common multiple of a collection of integers is the smallest positive integer that is evenly divisible by every integer in the collection. To find the least common multiple of a collection of integers, evaluate the function $\limfunc$lcm applied to the list of numbers enclosed in brackets and separated by commas. Leave the insertion point in the list and choose Evaluate.

$\blacktriangleright$ Evaluate

$\limfunc$lcm$\left(\vphantom{ 24,36}\right.$24, 36$\left.\vphantom{ 24,36}\right)$ =  72

$\limfunc$lcm$\left(\vphantom{ 35,15,65}\right.$35, 15, 65$\left.\vphantom{ 35,15,65}\right)$ = 1365

You can enter the function $\limfunc$lcm from the keyboard while in mathematics mode. It changes to gray, nonitalic letters on your screen. (If it does not appear on the function list under itbpF0.2992in0.3001in0.0692infunction.wmf, you can add it to the list.)

You can also determine both the greatest common divisor and least common multiple by inspection after applying Factor to each of the numbers in the list.