Find 5 common multiples of the following pairs of numbers. (a) 2 and 3 (b) 5 and 8 (c) 2 and 4 (d) 3 and 9 (e) 5 and 10 (f) 9 and 12 (g) 8 and 12 (h) 6 and 8 (i) 6 and 9
(a) 2 and 3: Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18... Multiples of 3: 3, 6, 9, 12, 15, 18... ∴ Common: 6, 12, 18, 24, 30
(b) 5 and 8: Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40... Multiples of 8: 8, 16, 24, 32, 40... ∴ Common: 40, 80, 120, 160, 200
(c) 2 and 4: Multiples of 4 are also multiples of 2. ∴ Common: 4, 8, 12, 16, 20
(d) 3 and 9: Multiples of 9 are also multiples of 3. ∴ Common: 9, 18, 27, 36, 45
(e) 5 and 10: Multiples of 10 are also multiples of 5. ∴ Common: 10, 20, 30, 40, 50
(f) 9 and 12: LCM = 36 ∴ Common: 36, 72, 108, 144, 180
(g) 8 and 12: LCM = 24 ∴ Common: 24, 48, 72, 96, 120
(h) 6 and 8: LCM = 24 ∴ Common: 24, 48, 72, 96, 120
(i) 6 and 9: LCM = 18 ∴ Common: 18, 36, 54, 72, 90
Explanation
The chapter explains that common multiples are numbers that appear in the multiplication tables of both numbers. To find common multiples, we list multiples of each number and find the numbers that appear in both lists. The first common multiple is called the Least Common Multiple (LCM).
Solution Steps
For (a) 2 and 3: Multiples of 2: 2,4,6,8,10,12,14,16,18... Multiples of 3: 3,6,9,12,15,18... Common: 6,12,18,24,30
For (b) 5 and 8: Multiples of 5: 5,10,15,20,25,30,35,40... Multiples of 8: 8,16,24,32,40... Common: 40,80,120,160,200
For (c) 2 and 4: Multiples of 4 are also multiples of 2. Common: 4,8,12,16,20
For (d) 3 and 9: Multiples of 9 are also multiples of 3. Common: 9,18,27,36,45
For (e) 5 and 10: Multiples of 10 are also multiples of 5. Common: 10,20,30,40,50
For (f) 9 and 12: LCM = 36. Common: 36,72,108,144,180
For (g) 8 and 12: LCM = 24. Common: 24,48,72,96,120
For (h) 6 and 8: LCM = 24. Common: 24,48,72,96,120
For (i) 6 and 9: LCM = 18. Common: 18,36,54,72,90