Math worksheet for practicing finding the least common multiple of monomials.

To find the Least Common Multiple (LCM) of monomials, we need to find the LCM of their numerical coefficients and the highest power of each variable present in the monomials.

Let's solve each pair step by step:

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1. 4L, 20k²

- Numerical part: LCM(4, 20) = 20
- Variables: L has no other L → keep L; k appears only in second term → keep k²
→ LCM = 20Lk²

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2. 4g³h⁵j, 8g²h³

- Numbers: LCM(4, 8) = 8
- g: max exponent is 3 → g³
- h: max exponent is 5 → h⁵
- j: only in first → include j¹
→ LCM = 8g³h⁵j

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3. 18m²n³, 54n⁴p²

- Numbers: LCM(18, 54) = 54
- m: only in first → m²
- n: max exponent is 4 → n⁴
- p: only in second → p²
→ LCM = 54m²n⁴p²

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4. a⁴b²c, b³a²

Rewrite as: a⁴b²c, a²b³

- Numbers: both have coefficient 1 → LCM = 1
- a: max exponent 4 → a⁴
- b: max exponent 3 → b³
- c: only in first → c¹
→ LCM = a⁴b³c

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5. 12x⁶y, 28x²y³

- Numbers: LCM(12, 28)
- 12 = 2²×3, 28 = 2²×7 → LCM = 2²×3×7 = 84
- x: max exponent 6 → x⁶
- y: max exponent 3 → y³
→ LCM = 84x⁶y³

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6. 9x³, 17x

- Numbers: LCM(9, 17) = 153 (since 9 and 17 are coprime)
- x: max exponent 3 → x³
→ LCM = 153x³

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7. 45uv, 21u²v³

- Numbers: LCM(45, 21)
- 45 = 3²×5, 21 = 3×7 → LCM = 3²×5×7 = 315
- u: max exponent 2 → u²
- v: max exponent 3 → v³
→ LCM = 315u²v³

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8. 72w², 96w³u

- Numbers: LCM(72, 96)
- 72 = 2³×3², 96 = 2⁵×3 → LCM = 2⁵×3² = 32×9 = 288
- w: max exponent 3 → w³
- u: only in second → u¹
→ LCM = 288w³u

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9. 24s³t², 56s⁴

- Numbers: LCM(24, 56)
- 24 = 2³×3, 56 = 2³×7 → LCM = 2³×3×7 = 168
- s: max exponent 4 → s⁴
- t: only in first → t²
→ LCM = 168s⁴t²

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10. 48ab²c³, 22a³bc

- Numbers: LCM(48, 22)
- 48 = 2⁴×3, 22 = 2×11 → LCM = 2⁴×3×11 = 16×33 = 528
- a: max exponent 3 → a³
- b: max exponent 2 → b²
- c: max exponent 3 → c³
→ LCM = 528a³b²c³

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Final Answer:
1. 20Lk²
2. 8g³h⁵j
3. 54m²n⁴p²
4. a⁴b³c
5. 84x⁶y³
6. 153x³
7. 315u²v³
8. 288w³u
9. 168s⁴t²
10. 528a³b²c³