Co ARITHMETIC. 



least number, which can be so measured, it is called their 

 lea'it common multiple % thus 30, 45, ^o and 75, are multi- 

 ples of 3 and 5 \ but their least common multiple is 15.* 



PROBLEM I. 



t 

 To find the greatest common measure of two or more niimhers., 



RULE.f 



I. If there be two numbers only, divide the greater 

 by the less, and this divisor by the remainder, and so on ; 

 always dividing the last divisor by the last remainder, till 



nothing 



* A prime rMmber is that, which can only be measured by an 

 unit. 



That number, which is produced by multiplying several numbers 

 together, is called a composite number. . 



A perfect number is equal to the sum of all its aliquot parts. 



The following perfect numbers are taken from the Petersburg!! 

 acts, and are all that are known at preseat. 

 6 



496 



8128 



3355^33^ 



8589869056 



137438691328 



2305843008 139952 1 28 



2417851639228158837784576 



99035 203 1428297 1 8304488 1 61 28 



There are several other numbers, which have received different 

 denominations, but they are principally of use in Algebra, and the 

 higher parts of mathematics. 



-j- This and the following problem will be found very useful in 

 the doctrine of fractions, and several other parts of Arithmetic. 



The truth of the rule may be shewn from the first example.— 

 For since 54 measures 308, it also measures 108 + 54, or 162. 



A gain > 



