Find the LCM and HCF of 12 and 68

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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

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