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2172                                                                 ARITHMETIC

11.   Mr. Smith walks 17 miles in 5 hours. At the same rate how many miles will he walk in 20 hours f in 25 hours ? in 40 hours f

12.   My lot of land is f as large as my neighbor's lot, which contains 17,500 square feet. How many square feet are there in my lot f

13.   Mr. A. is worth f as much as Mr. B.   If Mr. A. is worth $6000, how much is Mr. B. worth!

LEAST COMMON MULTIPLE.

A multiple of a number is a number that is exactly divisible by it. 3X5=15. 15 is a multiple of both 3 and 5.

A multiple of a number is larger than the number, except when it is the number itself.

Multiples of 8 are 8, 16, 24, 32? 40, 48, 56, 64, 72, etc. Multiples of 12 are 12, 24, 36, 48, 60, 72, etc.

We notice in the above multiples of 8 and 12, that 24, 48, and 72 are common to both. 24 is the smallest common multiple, and we call it the least common multiple.

The least common multiple (L. C. M.) of two or more numbers is the least number that is a multiple of each of them.

The least common multiple of two or more numbers is the product of their prime factors, each factor being used the greatest number of times it is lound in any of the numbers.

Find the L. C. M. of 8, 12, and 20.

The greatest number of times 2 is used as a factor in any number is 3 times.

The greatest number of times 3 is used is once. The greatest number of times 5 is used is once. The L. C. M. of 8, 12, and 20 is 2x2X2X3X5=120.

Another method of finding the L. C. M. is to divide by any prime number that will divide one or more of the numbers.

When one or more of the numbers are not divisible, bring them down without changing them.

Continue to divide until all the quotients are 1.

The product of all the divisors will be the L. C. M. 2X2X2X3X5=120 L. C. M.

8=2X2X2 12=2X2X3 20=2X2X5

2)8—12—20 2)4— 6—10

'  2)2— 3— 5 3)1_ 3— 5

5)1— 1— 5 1— 1— 1