LCM of 12 and 18: How to find LCM of 12 and 18?

The LCM of 12 and 18 is 36. Least common multiple (LCM) of two numbers is the smallest value, which is a multiple of both. The LCM of 12 and 18 is the smallest number that both 12 and 18 can divide evenly into. In this blog, we will go through different techniques to determine the LCM of 12 and 18 efficiently.

Ways to Determine the LCM of 12 and 18

There are several techniques to find the LCM of 12 and 18. Below are the most commonly used methods:

1. Prime Factorization Method

This approach involves breaking down numbers into their prime factors and taking the highest power of each factor.

• Prime factorization of 12: 2 × 2 × 3
• Prime factorization of 18: 2 × 3 × 3
• Selecting the highest powers of all prime factors: 2² × 3² = 36

Thus, LCM(12,18) = 36.

2. Listing Multiples Method

In this method, we list the multiples of each number and identify the smallest common multiple.

• Multiples of 12: 12, 24, 36, 48, 60, ...
• Multiples of 18: 18, 36, 54, 72, 90, ...
• The smallest number that appears in both lists is 36.

Thus, LCM(12,18) = 36.

3. Division Method

This method involves dividing both numbers by their common prime factors until only 1 remains.

1. Divide 12 and 18 by 2 → (6, 9)
2. Divide 6 and 9 by 3 → (2, 3)
3. 2 and 3 are only divisible by 1
4. Multiply all divisors together: 2 × 2 × 3 × 3 = 36

Thus, LCM(12,18) = 36.

Conclusion

The LCM of 12 and 18 is 36, and it can be determined through different methods such as prime factorization, listing multiples, and the division method.