LCM of 12 and 10
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 12 and 10. To solve this, we will identify the multiples of both numbers and determine the smallest multiple they share.
Answer
60
Answer for screen readers
The least common multiple of 12 and 10 is 60
Steps to Solve
-
Factorize each number into primes
Find the prime factorization of each number.
- $12 = 2^2 imes 3$
- $10 = 2 imes 5$
- Identify the highest powers of all prime factors
Collect the highest powers of all primes appearing in the factorizations.
- Highest power of 2: $2^2$
- Highest power of 3: $3$
- Highest power of 5: $5$
- Multiply these highest powers together
Multiply the highest powers of all the primes to get the LCM.
- $2^2 imes 3 imes 5 = 4 imes 3 imes 5 = 60$
The least common multiple of 12 and 10 is 60
More Information
The LCM is useful in finding common denominators for adding fractions and solving problems involving periodic events.
Tips
A common mistake is to take the least or only one of each prime factor instead of the highest powers.
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