Let’s solve each problem step by step. We’re finding the
Least Common Multiple (LCM) of pairs of numbers.
The LCM is the smallest number that both numbers divide into evenly.
We’ll go one by one:
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1) LCM(9, 15)
Multiples of 9: 9, 18, 27, 36,
45, 54...
Multiples of 15: 15, 30,
45, 60...
→ First common multiple is
45
✔ LCM(9, 15) =
45
---
2) LCM(4, 8)
Multiples of 4: 4, 8, 12, 16...
Multiples of 8: 8, 16, 24...
→ First common multiple is
8
✔ LCM(4, 8) =
8
---
3) LCM(6, 5)
Multiples of 6: 6, 12, 18, 24,
30, 36...
Multiples of 5: 5, 10, 15, 20, 25,
30, 35...
→ First common multiple is
30
✔ LCM(6, 5) =
30
---
4) LCM(22, 6)
Multiples of 22: 22, 44,
66, 88...
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60,
66, 72...
→ First common multiple is
66
✔ LCM(22, 6) =
66
---
5) LCM(8, 27)
These have no common factors except 1 → so LCM = 8 × 27 =
216
Check:
Multiples of 8: 8, 16, 24, ..., 216
Multiples of 27: 27, 54, 81, 108, 135, 162, 189,
216
→ Yes, 216 is first common
✔ LCM(8, 27) =
216
---
6) LCM(2, 3)
Multiples of 2: 2, 4,
6, 8...
Multiples of 3: 3,
6, 9...
→ First common is
6
✔ LCM(2, 3) =
6
---
7) LCM(14, 4)
Multiples of 14: 14, 28, 42...
Multiples of 4: 4, 8, 12, 16, 20, 24,
28, 32...
→ First common is
28
✔ LCM(14, 4) =
28
---
8) LCM(5, 21)
No common factors → LCM = 5 × 21 =
105
Check:
Multiples of 5: 5, 10, 15, ..., 105
Multiples of 21: 21, 42, 63, 84,
105
→ Correct
✔ LCM(5, 21) =
105
---
9) LCM(14, 6)
Multiples of 14: 14, 28,
42, 56...
Multiples of 6: 6, 12, 18, 24, 30, 36,
42, 48...
→ First common is
42
✔ LCM(14, 6) =
42
---
10) LCM(12, 20)
Multiples of 12: 12, 24, 36, 48,
60, 72...
Multiples of 20: 20, 40,
60, 80...
→ First common is
60
✔ LCM(12, 20) =
60
---
Final Answer:
1) 45
2) 8
3) 30
4) 66
5) 216
6) 6
7) 28
8) 105
9) 42
10) 60
Parent Tip: Review the logic above to help your child master the concept of least common denominator worksheet.
