LCM of 21 and 28
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 21 and 28. To solve this, we will find the LCM by determining the multiples of each number and identifying the smallest common multiple.
Answer
84
Answer for screen readers
The least common multiple of 21 and 28 is 84.
Steps to Solve
- Find the prime factors of each number
To find the least common multiple (LCM), first determine the prime factors of each number.
For 21: $21 = 3 imes 7$
For 28: $28 = 2^2 imes 7$
- Identify the highest power of each prime factor
The LCM is found by using the highest power of each prime factor that appears in the factorization of either number.
The prime factors are 2, 3, and 7. The highest powers are: $2^2$ from 28, $3$ from 21, $7$ (appears in both).
- Multiply the highest powers of the prime factors
To find the LCM, multiply the highest powers of all the prime factors together:
$$LCM = 2^2 imes 3 imes 7$$ $$LCM = 4 imes 3 imes 7$$ $$LCM = 12 imes 7$$ $$LCM = 84$$
The least common multiple of 21 and 28 is 84.
More Information
The least common multiple (LCM) of two numbers is the smallest positive integer that is divisible by both the numbers. In this case, the LCM of 21 and 28 is 84.
Tips
A common mistake is to not use the highest power of each prime factor when multiplying to find the LCM. Ensure you take the largest power of each prime number that is present in the prime factorizations of the given numbers.
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