https://file.aiquickdraw.com/mathbot/file/1727457733468r1j5ojoq.jpg

The problem in the image asks to find the HCF (Highest Common Factor) and LCM (Least Common Multiple) of 12, 18, and 36 using the common division method.

### Steps to solve using the common division method:

#### Step 1: Write the numbers
We have to find the HCF and LCM of 12, 18, and 36. We arrange these numbers together:

12, 18, 36

#### Step 2: Start dividing by common prime factors
Begin dividing the numbers by a common prime factor until no further division is possible.

- Divide all numbers by 2 (since 2 is a factor of all):
  \[
  12 \div 2 = 6, \quad 18 \div 2 = 9, \quad 36 \div 2 = 18
  \]
  Result: 6, 9, 18

- Divide again by 2:
  \[
  6 \div 2 = 3, \quad 9 \div 2 \text{ (not divisible)}, \quad 18 \div 2 = 9
  \]
  Result: 3, 9, 9

- Now divide by 3 (next common prime factor):
  \[
  3 \div 3 = 1, \quad 9 \div 3 = 3, \quad 9 \div 3 = 3
  \]
  Result: 1, 3, 3

- Divide again by 3:
  \[
  1 \div 3 = 1, \quad 3 \div 3 = 1, \quad 3 \div 3 = 1
  \]
  Result: 1, 1, 1 (end of division process)

#### Step 3: HCF and LCM calculations

- **HCF**: Multiply the common prime factors used in all steps.
  \[
  HCF = 2 \times 3 = 6
  \]

- **LCM**: Multiply all divisors (prime factors used in any step):
  \[
  LCM = 2 \times 2 \times 3 \times 3 = 36
  \]

### Final Answer:
- **HCF** of 12, 18, and 36 = 6
- **LCM** of 12, 18, and 36 = 36

Would you like further details or clarifications?

### Related questions:
1. How do you find the HCF of two numbers using the prime factorization method?
2. Can the LCM of two numbers ever be smaller than both numbers?
3. How is the HCF related to the product of the two numbers and their LCM?
4. How does the common division method differ from using prime factorization?
5. How can we use the HCF to simplify fractions?

### Tip:
Always start dividing by the smallest prime factor (like 2) and continue with larger primes like 3, 5, etc., for efficiency in the common division method.

Find the HCF and LCM of 12, 18, and 36 using the common division method.

Step-by-step guide to finding the HCF and LCM of 12, 18, and 36 using the common division method. Learn the key mathematical concepts of prime factorization, division, and more. Suitable for Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation