Multiples : these are what we get after multiplying a number by an integer (not a decimal or fraction) Example : 6 * 1 = 6......6 * 2 = 12.....6 * 3 = 18......so 6,12, and 18 are multiples of 6.
factors : these are what we multiply by to get a number Example : 1 * 6 = 6.....so 1 and 6 are factors of 6....2 * 3 = 6 ...so 2 and 3 are also factors of 6 ============================== problem 1 : Look at ur clues...each number is less then or equal to 12....this right here eliminates D because of the 15. The greatest common factor of the 2 numbers is 2....and this eliminates B because if it has a factor of 2, it has to be an even number. So that leaves us with : A. 6 and 10 C. 10 and 12 last clue....they have a least common multiple of 60...this means that ur 2 numbers cant have any other common multiples until 60. 6 * 10......both are multiples of 60...however, they are also both multiples of 30...so 60 is not the least common multiple of 6 and 10, it is 30. Therefore, ur answer is C. 10 and 12....with the LCM of 60, LCF of 2 and < or = to 12 =================== problem 2 : GCF (greatest common factor) of 42 and 84
factors of 42 : 1,2,3,6,7,14,21,42 factors of 84 : 1,2,3,4,6,7,12,14,21,28,42,84
Assuming R and H: So volume is pir^2 * H = 1500 and H = 1500/(pir^2) while surface area is A= 2pir*H + 2pir^2 A = 2pir(r+h)= 2piR^2 + 2pir*1500/(pir^2)= 2piR^2 + 3000/r For A to take minimum, get the derivative 4pir - 3000/R^2 and let it be 0 4pir^3 - 3000 = 0 r = cbrt(3000/(4pi)) ≈ 6.20 h = 1500/(pi(6.20)^2) ≈ 12.42
