How to find the LCM of a number?
Understand the Problem
The question is asking how to calculate the least common multiple (LCM) of a number, which generally involves using the prime factorization of the numbers or listing the multiples until a common one is found.
Answer
$36$
Answer for screen readers
The least common multiple (LCM) of 12 and 18 is $36$.
Steps to Solve
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Identify the numbers involved Determine the numbers for which you want to find the least common multiple (LCM). For example, let's say we want to find the LCM of 12 and 18.
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Prime Factorization Factor each number into its prime factors.
For 12:
$$ 12 = 2^2 \cdot 3^1 $$
For 18:
$$ 18 = 2^1 \cdot 3^2 $$
- Take the highest powers of all prime factors Identify all the prime factors used in the factorization and take the highest exponent for each.
- For $2$: the highest power is $2^2$ (from 12).
- For $3$: the highest power is $3^2$ (from 18).
- Multiply the highest powers together Combine these highest powers to find the LCM.
$$ \text{LCM} = 2^2 \cdot 3^2 $$
- Calculate the product Now perform the multiplication:
$$ \text{LCM} = 4 \cdot 9 = 36 $$
The least common multiple (LCM) of 12 and 18 is $36$.
More Information
The least common multiple is useful in many areas of mathematics, such as adding and subtracting fractions with different denominators or solving problems involving periodic events. The LCM is the smallest number that is a multiple of both original numbers.
Tips
- Not fully factoring the numbers into their prime factors.
- Using the wrong exponent when selecting the highest power of a prime factor.
- Forgetting to multiply the highest power primes together to find the LCM.
