1. c. m. the greatest number of 2's, 3's, 5's, 7's, etc., fo any one of the numbers. 24 has the greatest number of 2's as factors. 50 has the greatest number of 5's as factors. 35 is the only number in which the factor 7 occurs. There must be as many 2's among the factors of the 1. c there are 2's among the factors of 24; as many 3's as there among the factors of 36; as many 5's as there are 5's amo factors of 50; as many 7's as there are 7's among the factors that is, three 2's, two 3's, two 5's, and one 7. Find the 1. c. m. 7. Of 48 and 60. 9. Of 50 and 60. 11. Of 20, 30, and 40 12. Of 40, 50, and 60 13. Of 24, 48, and 36 14. Of 25, 35, and 40 Observe that in multiplying the sum of two numbers b number, the sum may be found and multiplied; or each num be multiplied and the sum of the products found. 1. In the last three examples given above, let a = 5 and c = 2; then perform again the operations indicat compare the results with those obtained when the were employed. Observe that in multiplying the difference of two numb third number, the difference may be found and multiplied; number may be multiplied and the difference of the product 2. In the last three problems given above, let a = 5 and c = 2; then perform again the operations indicat compare the results with those obtained when the were employed. 157. PROBLEMS. 5, b = 3, and c = 2, find the value of the foll *This means, that the sum of 7 and 4 is to be multiplied by six; or that of six 7's and six 4's is to be found. + This means, that the difference of 7 and 4 is to be multiplied by six; or difference of six 7's and six 4's is to be found. 1. The sum of the angles of any triangle is equal to 2. In a right triangle there is one right angle. The other two angles are together equal to 3. In a right triangle one of the angles is an angle of 40°. How many degrees in each of the other two angles? Draw such a triangle. 4. Convince yourself by drawings and measurements that every equilateral triangle is equiangular. EQUILATERAL TRIANGLES. EQUIANGULAR TRIANGLES. 5. Note that in every equiangular triangle each angle is one third of 2 right angles. So each angle is an angle of degrees. 6. If any one of the angles of a triangle is greater or less than 60, can the triangle be equiangular? Can it be equilateral? 7. If angle a of an isosceles triangle mea-. sures 50°, how many degrees in angle b? in angle c? * See p. 59. b a third angle. Draw such a triangle. 3. Let a equal the number of degrees in one ang triangle and b equal the number of degrees in another of the same triangle; then the number of degrees third angle is 180° – (a + b). If a equals 30, and b 45, how many degrees in the third angle? Draw s triangle. 4. Name four multiples of 16. 5. Name three common multiples of 16 and 12. 6. Name the least common multiple of 16 and 12. 7. Find the sum of all the prime numbers from 101 inclusive. 8. Find the prime factors of 836. 9. With the prime factors of 836 in mind or repres on the blackboard, tell the following: (a) How many times is 19 contained in 836 ? (b) How many times is 209, (11 × 19), contained in (c) How many times is 418, (19 × 11 × 2), contained in |