The following is another method of finding the 1. c. m., although the principle is the same. 26 20 45 33 10 45 51 10 15 2 3 1. c. m.=2×3×5×2×3=180. This method consists only in a briefer arrangement of the following work which we should do in finding the prime factors of each number separately: 91. Find the l. c. m. of 21, 33, and 28. 3/21 33 28 77 11 28 1 11 4 Ans.3× 7 × 11 × 4. 92. Find the l. c. m. of 100, 400, and 1000. divide by its prime factors one after the other. 93. Find the l. c. m. of 8 and 12. 94. Find the l. c. m. of 8 and 14. 95. Find the l. c. m. of 9 and 15. 96. Find the l. c. m. of 15 and 18. 97. Find the l. c. m. of 10, 14, and 15. 98. Find the l. c. m. of 15, 24, and 35. 99. Find the l. c. m. of 30, 48, and 56. 100. Find the l. c. m. of 32, 72, and 120. 101. Find the l. c. m. of 42, 60, and 125. 102. Find the l. c. m. of 250, 180, and 540. 103. Reduce and to the least common de nominator and then add them together. 18 104. Reduce and to the least common denominator and then add them together. 105. Reduce, 16, 24, and to their least common denominator. 106. Find the greatest common divisor of 48 and 130. 107. Reduce 17 ,,, and to their least com mon denominator. 18 108. Subtract 154 from 183. 109. Reduce and to the least common de nominator and then add them. 110. Reduce and 1 to the least common 5 14 nominator and then add them. de to the least common denominator and then add them. 5 112. Reduce and to the least common denominator and then add them. 113. Reduce 2 and 4 to the least common denominator and then add them. 114. Reduce,, and to the least 17 90 denominator and then add them. common 115. Reduce, §, 12, and 2 to the least com*[116. a. Find the l. c. m. of 407 and 481. In a case of this kind, where none of the prime factors of either number can be found by inspection, it is best to find first the g. c. d. In this example we shall find the g. c. d. to be 37, which is contained 11 407 and 13 times in 481... (407 = 11×37 )481=13×37 mon denominator and then add them. times in and the l. c. m. is 11 × 13 × 37=5291. 120. Find the l. c. m. of 17 and 31 and 2. 121. Find the l. c. m. of 7, 13, and 3. NOTE. Where, as in the last two examples, two or more numbers have no common factors, their l. c. m. is evidently their product. 122. Find the l. c. m. of 3, 13, and 31. 123. What is the l. c. m. of 20, 24, and 36? 124. Add, 2 ,, 215, and 3%. 20 *[125. What is the g. c. d. of 1181 and 2741?]* 3 126. Reduce, 1, and to a common denominator. 127. Name all the prime numbers in the series of numbers from 1 to 29; resolve all the composite numbers into their prime factors; and name all the perfect squares. 128. Add together,, and, and from their sum subtract 15. 129. a. Find the g. c. d. of 12, 30, and 45. [The g. c. d. of 12 and 30 is 6; and the g. c. d. of 6 and 45 is 3. Therefore the answer is 3.] b. Find the g. 130. Reduce c. d. of 720, 336, and 1736. 448 to its lowest terms. 29400 4 60 131. Reduce 0, 12, 15, 25, and to their least common denominator, add them and reduce the sum to its simplest form. 132. Find the g. c. d. and the l. c. m. of 630, 840, and 2772. 133. Find the g. c. d. and l. c. m. of 144 and 780. 7 134. Reduce, 8, 15, and 1 to their least common denominator. 135. Subtract 154 from 183. 136. Reduce 23820 to its lowest terms. 39700 137. What is the g. c. d. of the two numbers 4760 and 3432? 138. What is the l. c. m. of 48, 98, 21, and 27? 139. What is the g. c. d. of 1872 and 432? [Obtain the answer by factoring.] 140. Find the g. c. d. of 187 and 153; also their l. c. m. SECTION Χ. CANCELLATION AND ANALYSIS. 1. How many tons of coal at $6 a ton can be bought for 15 tons of hay at $18 a ton? Solution: 15 tons of hay at $18 a ton is worth 15 × 18 dollars, or $270. As many tons of coal at $6 a ton can be bought for $270 as 6 is contained in 270, or 45 tons. The answer just found was got by dividing 15 times 18 by 6. We may say, then, that the an15 × 18 tons. Now, dividing both swer is equal to 6 the dividend and the divisor first by 3, and then some time and labor. Striking out the common factors from the divisor and dividend is called CANCELLATION. 2. If 6 men can build a stone wall 40 ft. long, 5 ft. high, and 2 ft. thick in 6 days, how long will it take them to build a wall 80 ft. long, 5 ft. high, and 3 ft. thick? |