LEATHER 

 ?ind the L, C. M. of 78, 91, 104. 



] 



3359 



LEATHER 



78 = 2X3X13 

 91 = 7X13 

 104 = 2X2X2X13 



The L. C. M.=2X2X2X7X3X13. 

 Note that the 



in 78 is not used in the L. C. 



M because 2 occurs as a factor in 104, which is 

 found in 2X2X2X13. The factor "7" of 91 

 must be used and "3" of 78 so that the multiple 

 will contain 7X13 and 3X13. Look for the fac- 

 tors of 78 in the L. C. M. above. You find 2X3 

 X 13 Look for the factors of 91. You find 7X13. 

 Look for the factors of 104. You find 2X2X2X 

 13. Having found the L. C. M. of any set of 

 numbers, always find in it the factors of each 

 number. 



(2) Find the L. C. M. of 300, 252 and 540. 



300 = 2X2X3X5X5 

 252 = 2X2X3 X3X7 

 540 = 2X2X3X3X3X5 



The L. C. M.=2X2X3X3X3X5X7X5. 



Note that the first six factors are the factors of 

 540 ; the factor "7" is the only factor of 252 not 

 in 540, and it must be used so that the L. C. M. 

 will be divisible by 252 ; a second 5 is the only 

 factor of 300 not in 540 or in 252, and it must 

 be used so that the L. C. M. will be divisible by 

 300. 



Every prime factor of each number must be 

 found in the L. C. M., the greatest number of 

 times it occurs in any of the numbers. Put 

 into its usual form the rule is stated : 



The L. C. M. of several numbers is the product 

 of the different prime factors of the numbers, 

 each factor being used the greatest number of 

 times it occurs in any one of the numbers. This 

 is seen in the last problem above : 3 is a factor 

 of 540 three times; 2 is a factor of each of the 

 numbers twice ; 5 is a factor of 300 twice. There- 

 fore 3 occurs as a factor in the L. C. M. three 

 times, 2 occurs two times and 5 occurs two times. 



This factoring is sometimes done as follows: 

 Find the L. C. M. of 16, 54, 72. 



11 



1 7 



I 2 



The L. C. M.=2X2X2X3X3X2X3X1. 



Explanation. Find -any prime factor common 

 to two or more of the numbers ; divide by this 

 factor the numbers divisible by it, placing quo- 

 tients in the line below, and with them the undi- 

 vided numbers. Find a second prime factor, and 

 divide and bring down as before. Continue as 

 above until there is no factor common to any two 

 of the resulting numbers. The L. C. M. is the 

 product of all the divisors, quotients and undi- 

 vided numbers. A.H. 



LEATHER, leth'er, a 'commodity of the ut- 

 most service to mankind, made of the dressed 

 skins of animals. Savage man used the pelts 

 of wild beasts to protect him from the rigors 



of winter. Civilized man, for the most part, 

 wears leather only on his hands and feet, but 

 he has found many other invaluable commer- 

 cial uses for it. 



The untreated, dry skins of animals soon 

 rot. Primitive man learned how to prevent 

 this decay by treating hides with smoke, oils 

 and the brains of the animals themselves, later 

 resorting to certain astringent barks. The 

 process of dressing is now much more scien- 

 tific, skins being prepared for industrial use 

 by tanning, tawing, chamoising, and so on. 

 The hide of the animal consists of three layers, 

 but it is of the true skin, the middle layer of 

 gelatinous fibers, that leather is manufactured. 



When the tanner gets his hides they are 

 usually hard and inflexible. If they reach him 

 from a distance, he finds they have been pre- 

 served by salting or drying, and are hard and 

 stiff. To restore pliability, the hides are soaked 

 in water, of ten being subjected also to a knead- 

 ing process. The hair is then removed with 

 the aid of milk of lime, or one of several acids. 

 The skin is then ready for tanning. This is 

 accomplished by placing it in a vat containing 

 a solution made by soaking ground oak or 

 hemlock bark in boiling water, the strength of 

 the solution being gradually increased. The 

 tanning of large hides requires from four to 

 twelve months by this method, but for all 

 common uses leather is now tanned less slowly 

 by a chemical process. Sheepskins and goat- 

 skins are prepared by a process of tawing, bran 

 and alum being substituted for tanbark. This 

 produces the pliable leather used for gloves, 

 the uppers of shoes, etc. The soles of shoes 

 are made of the thick parts of horsehide or 

 cowhide, found along the back of the animal. 

 From goatskin various grades of kid and the 

 so-called Morocco, used in bookbinding, are 

 obtained. 



The leather manufactured in the United 

 States is the best in the world, and it is an 

 important article of export. However, the 

 best skins in the world are grown on sheep in 

 the Caucasus Mountains region of Europe. 



Artificial Leather, a term applied to sub- 

 stances which resemble leather and are substi- 

 tuted for it. Leather is a costly commodity, 

 and since the demand for it is great the inge- 

 nuity of manufacturers put a substitute on the 

 market in 1849. This was then called leather 

 cloth. 'The process of manufacture is as fol- 

 lows : The cloth is covered with oily pigments, 

 is dried in a hot oven, and after being passed 

 between rollers, is covered with pumice dust. 



