GCF-LCM answers

In-class #1 answers
  1. Factors of 35: 1, 5, 7
    Factors of 25: 1, 5
    GCF = 5
  2. Factors of 14: 1, 2, 7, 14
    Factors of 28: 1, 2, 4, 7, 14
    GCF = 14
  3. Factors of 40: 1, 2, 4, 5, 8, 10, 20
    Factors of 18: 1, 2, 3, 6, 9
    GCF = 2
  4. Factors of 14: 1, 2, 7, 14
    Factors of 42: 1, 2, 3, 6, 7, 14, 21
    GCF = 14
  5. Factors of 18: 1, 2, 3, 6, 9
    Factors of 33: 1, 3, 11
    GCF = 3
  6. Factors of 24: 1, 2, 3, 4, 6, 8, 12
    Factors of 16: 1, 2, 4, 8
    GCF = 8
  7. LCM (35,25) = 875/5 = 175
  8. LCM (14,28) = 392/14 = 28
  9. LCM (40,18) = 720/2 = 360
  10. LCM (14,42) = 588/14 = 42
  11. LCM (18,33) = 594/3 = 198
  12. LCM (24,16) = 384/8 = 48
In-class #2 answers
  1. Multiples of 12: 12, 24, 36, 48, 60, 72
    Multiples of 20: 20, 40, 60, 80
    LCM = 60
  2. Multiples of 7: 7, 14, 21, 28, 35, 42
    Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36
    LCM = 28
  3. Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48
    Multiples of 10: 10, 20, 30, 40, 50
    LCM = 30
  4. Multiples of 4: 4, 8, 12, 16, 20, 24
    Multiples of 3: 3, 6, 9, 12, 15, 18
    LCM = 12
  5. Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100
    Multiples of 25: 25, 50, 75, 100, 125
    LCM = 50
  6. Multiples of 14: 14, 28, 42, 56, 70
    Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48
    LCM = 42
  7. GCF(12,20) = 240/60 = 4
  8. GCF(7,4) = 28/28 = 1
  9. GCF(6,10) = 60/30 = 2
  10. GCF(4,3) = 12/12 = 1
  11. GCF(10,25) = 250/50 = 5
  12. GCF(14,6) = 84/42 = 2
In-class #3 answers
  1. Using the LCM formula:
    LCM (a,b) = (a x b)/ GCF(a,b) = 192 / 4 = 48
  2. Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54.
    Multiples of 16 16: 16, 32, 48
    In 48 days she will do both on the same day.
  3. Factors of 14: 1, 2, 7, 14
    Factors of 8: 1, 2, 4, 8
    He can pack 2 CDs in each box.

Homework #1 answers
  1. Factors of 34: 1, 2
    Factors of 14: 1, 2, 7
    GCF = 2
  2. Factors of 51: 1,3, 17
    Factors of 17: 1, 17
    GCF = 17
  3. Factors of 42: 1, 2, 3, 7, 12, 21, 42
    Factors of 9: 1, 3, 9
    GCF = 3
  4. Factors of 18: 1, 2, 3, 6, 9, 18
    Factors of 12: 1, 2, 3, 4, 6, 12
    GCF = 6
  5. Factors of 30: 1, 2, 3, 5, 6, 15, 30
    Factors of 42: 1, 2, 3, 6, 7, 21, 42
    GCF = 6
  6. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
    Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
    GCF = 12
  7. LCM(34,14) = 476/2 = 238
  8. LCM(51,17) = 867/17 = 51
  9. LCM(42,9) = 378/3 = 126
  10. LCM(18,12) = 216/6 = 36
  11. LCM(30,42) = 1260/6 = 210
  12. LCM(24,36) = 864/12 = 72
Homework #2 answers
  1. Multiples of 15: 15, 30, 45, 60, 75, 90
    Multiples of 25: 25, 50, 75, 100
    LCM = 75
  2. Multiples of 14: 14, 28, 42, 56
    Multiples of 28: 28, 56
    LCM = 28
  3. Multiples of 40: 40, 80 120, 160, 200
    Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120
    LCM = 120
  4. Multiples of 48: 48, 96, 144
    Multiples of 32: 32, 64, 96
    LCM = 96
  5. Multiples of 20: 20, 40, 60, 80, 100
    Multiples of 25: 25, 50, 75, 100
    LCM = 100
  6. Multiples of 8: 8, 16, 24, 32, 40, 48, 56
    Multiples of 28: 28, 56
    LCM = 56
  7. GCF(15,25) = 375/75 = 5
  8. GCF(14,28) = 392/28 = 14
  9. GCF(40,15) = 600/120 = 5
  10. GCF(48,32) = 1536/96 = 16
  11. GCF(20,25) = 500/100 = 5
  12. GCF(8,28) = 224/56 = 4
Homework #3 answers
  1. Multiples of 20: 20, 40, 60
    Multiples of 8: 8, 16, 24, 32, 40, 48
    LCM = 40.
    In order to have 40 of each item, Juan should buy 2 bags of balloons and 5 packages of candy bars.
  2. Multiples of 12: 12, 24, 36, 48, 60, 72
    Multiples of 15: 15, 30, 45, 60, 75
    The 60th caller will win both.
  3. Factors of 81: 1, 3, 9, 27, 81
    Factors of 63: 1, 3, 7, 9, 21, 63
    I can put 9 in a row.
  4. GCF (a,b) = (a x b) / LCM(a,b)
        6 = (18 x b) / 36
        18b = 216
        b = 216/18 = 12