What is the L.CM of a 8 and 12 b 16 und 20 c 214 and 18

Question

UpStudy AI · Accepted Answer

It looks like you're asking for the **Least Common Multiple (LCM)** of the following pairs of numbers:

a) 8 and 12  
b) 16 and 20  
c) 214 and 18

Let's calculate each one step by step.

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### a) LCM of 8 and 12

**Prime Factorization:**
- 8 = 2³
- 12 = 2² × 3¹

**LCM Calculation:**
Take the highest power of each prime factor present in either number:
- 2³ (from 8)
- 3¹ (from 12)

**LCM = 2³ × 3¹ = 8 × 3 = 24**

**So, LCM(8, 12) = 24**

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### b) LCM of 16 and 20

**Prime Factorization:**
- 16 = 2⁴
- 20 = 2² × 5¹

**LCM Calculation:**
Take the highest power of each prime factor present in either number:
- 2⁴ (from 16)
- 5¹ (from 20)

**LCM = 2⁴ × 5¹ = 16 × 5 = 80**

**So, LCM(16, 20) = 80**

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### c) LCM of 214 and 18

**Prime Factorization:**
First, factorize each number.

- **214:**
  - 214 ÷ 2 = 107
  - 107 is a prime number.
  - So, 214 = 2¹ × 107¹

- **18:**
  - 18 = 2¹ × 3²

**LCM Calculation:**
Take the highest power of each prime factor present in either number:
- 2¹ (common to both)
- 3² (from 18)
- 107¹ (from 214)

**LCM = 2¹ × 3² × 107¹ = 2 × 9 × 107 = 2 × 963 = 1926**

**So, LCM(214, 18) = 1926**

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### Summary

- **a) LCM(8, 12) = 24**
- **b) LCM(16, 20) = 80**
- **c) LCM(214, 18) = 1926**

If you need further explanations or assistance with other problems, feel free to ask!
The LCMs are: - a) 24 - b) 80 - c) 1926

Real Tutor Solution