Find the LCM and HCF of 12 and 68

Question

UpStudy AI · Accepted Answer

To find the **Highest Common Factor (HCF)** and **Least Common Multiple (LCM)** of the numbers **12** and **68**, you can use the following methods:

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### **1. Highest Common Factor (HCF)**
The HCF of two numbers is the largest number that divides both of them without leaving a remainder.

**Method: Euclidean Algorithm**

1. **Divide the larger number by the smaller number** and find the remainder.
   
   $$
   68 \div 12 = 5 \text{ with a remainder of } 8
   $$

2. **Replace** the larger number with the smaller number and the smaller number with the remainder.
   
   Now, find the HCF of **12** and **8**.

3. **Repeat the process**:
   
   $$
   12 \div 8 = 1 \text{ with a remainder of } 4
   $$
   
   Now, find the HCF of **8** and **4**.

4. **Continue until the remainder is 0**:
   
   $$
   8 \div 4 = 2 \text{ with a remainder of } 0
   $$
   
   When the remainder is **0**, the divisor at this step (**4**) is the HCF.

**So, HCF of 12 and 68 is 4.**

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### **2. Least Common Multiple (LCM)**
The LCM of two numbers is the smallest number that is a multiple of both.

**Formula Method:**

$$
\text{LCM}(a, b) = \frac{a \times b}{\text{HCF}(a, b)}
$$

Using the HCF we found:

$$
\text{LCM}(12, 68) = \frac{12 \times 68}{4} = \frac{816}{4} = 204
$$

**So, LCM of 12 and 68 is 204.**

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### **Summary**

- **HCF (Highest Common Factor)** of 12 and 68 is **4**.
- **LCM (Least Common Multiple)** of 12 and 68 is **204**.
The HCF of 12 and 68 is 4, and the LCM is 204.

Find the LCM and HCF of
12 and 68

Upstudy AI Solution

Answer

Solution

1. Highest Common Factor (HCF)

2. Least Common Multiple (LCM)

Summary

Bonus Knowledge

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