LEASE 



3358 



LEAST COMMON MULTIPLE 



29 "leaps" over the day of the week on which 

 it would fall in ordinary years. For example: 

 if March 1 falls on Monday in one year it 

 will fall on Tuesday in the next, if that is an 

 ordinary year of 365 days, but on Wednesday 

 if it is leap year. Leap years are those which 

 may be exactly divided by four, except that 

 years ending with two ciphers are leap years 

 only when they are divisible by 400. See 

 CALENDAR. 



LEASE, leese, a contract or conveyance for 

 the possession and profits of land or other 

 property for a stated period. The party grant- 

 ing the lease is called the lessor; the party to 

 whom it is granted is the lessee, or tenant; the 

 fixed compensation received in return for the 

 use, possession and profit of the property is 

 called the rent. A lease for life terminates 

 with the death of the lessee, while a lease for 

 a term of years begins and ends at a certain 

 specified date. Under a lease for a long period 

 the tenant possesses greater privileges, as he 

 becomes the virtual owner of the premises and 

 is limited only by rules that govern the rela- 

 tions of landlord and tenant. Rents may be 

 payable in valuables other than money, such 

 as produce, but this is unusual; indeed, fre- 

 quently the terms of a lease specify that the 

 rental shall be payable in gold, to guard against 

 possibility of having to accept a depreciated 

 currency, which would lower the income de- 

 rived from the property. The essential specifi- 

 cations in a written lease are dates, names, 

 rent and description of property. A lease for 

 a period of from one year or less may be by 

 verbal contract, but it must be in writing if 

 for a longer period. See CONTRACT; TENANT. 



LEAST COMMON MULTIPLE, the least 

 number that will contain two or more numbers 

 without a remainder. 



What number of pennies can be divided ex- 

 actly into groups of two pennies each or groups 



Three twos 



IO0OI0O0 



Two threes 



FIG. i 



of three pennies each? We can divide 6, 12, 

 18, 24 and so on into groups of 2's or groups 

 of 3's, as three twos, two threes (see Fig. 1). 



By a drawing show how 12 units and 18 

 units can be divided into groups. 



What number of yards of ribbon can be di- 

 vided exactly into 2-yard strips or 5-yard 

 strips (see Fig. 2)? Into strips of 10 yards, 

 20 yards, 30 yards and so on? 



zl I A 



I 



Show the same for 20, 30 and 40, by draw- 

 ings. 



6, 12, 18, etc., are multiples of 3 and 2. 10, 

 20, 30, etc., are multiples of 2 and 5. 



Because these numbers are multiples of two 

 numbers, they ar.e called common multiples 

 of the two numbers. Since 6 is the smallest 

 number that is a multiple of 2 and 3, and 10 

 is the smallest number that is a multiple of 2 

 and 5, 6 is called the least common multiple 

 of 2 and 3, and 10 is called the least common 

 multiple of 2 and 5. This term is abbreviated 

 L.C.M. 



How to Find a Least Common Multiple. 



(a) The L. C. M. of several numbers often may 

 be easily seen, as, of 2, 4, 8; 2, 5, 20; 5, 

 10, 30: 8 is the L.C.M. of 2, 4, 8; 20 is 

 the L. C. M. of 2, 5, 20; 30 is the L. C. M. 

 of 5, 10, 30. 



(b) The L. C. M. is often readily found, as be- 

 low, by seeing at once the greatest com- 

 mon factor of several numbers. 



(1) Find the L.C.M. of 15 and 24. 



15 = 5X3 

 24 = 8X3 



The L. C. M.=8X5X3; that is, 8X15 or 

 5X24. 



(2) Find the L. C. M. of 72 and 64. 



72 = 9X8 

 64 = 8X8 



The L. C. M.=8X9X8. 



(3) Find the L. C. M. of 77 and 99. 



77 = 7X11 

 99 = 9X11 



The L. C. M.=9X7X11. 



(4) Find the L. C. M.- of 72 and 96. 



72 = 3X24 

 96 = 4X24 



The L. C. M.=4X3X24. 



(c) The L. C. M. is found by factoring into 



prime factors. 



