LCM of 28 and 16
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 28 and 16. To solve this, we can find the multiples of both numbers and determine the smallest multiple that they have in common, or use the prime factorization method to calculate the LCM.
Answer
The LCM of 28 and 16 is $112$.
Answer for screen readers
The least common multiple (LCM) of 28 and 16 is $112$.
Steps to Solve
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Prime Factorization of 28
First, we find the prime factorization of 28.
28 can be divided by 2:
$$ 28 \div 2 = 14 $$
14 can be divided by 2 again:
$$ 14 \div 2 = 7 $$
7 is a prime number.
So, the prime factorization of 28 is:
$$ 28 = 2^2 \times 7^1 $$ -
Prime Factorization of 16
Next, we find the prime factorization of 16.
16 can be divided by 2 multiple times:
$$ 16 \div 2 = 8 $$
$$ 8 \div 2 = 4 $$
$$ 4 \div 2 = 2 $$
$$ 2 \div 2 = 1 $$
So, the prime factorization of 16 is:
$$ 16 = 2^4 $$ -
Finding the LCM
To find the LCM, we take the highest power of each prime number from the factorizations.
The primes we have are 2 and 7.
- The highest power of 2 is $2^4$.
- The highest power of 7 is $7^1$.
Thus, the LCM is:
$$ LCM = 2^4 \times 7^1 $$
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Calculate the LCM
Now we calculate it:
$$ LCM = 16 \times 7 = 112 $$
The least common multiple (LCM) of 28 and 16 is $112$.
More Information
The LCM is the smallest number that both given numbers divide evenly into. It's useful in various mathematical problems, such as finding common denominators in fractions or solving problems involving synchronized events.
Tips
- Confusing LCM with GCD (greatest common divisor). They serve different purposes.
- Forgetting to take the highest power of each prime factor when calculating the LCM.
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