lcm of 28 and 24
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 28 and 24. To find the LCM, we determine the multiples of each number and identify the smallest multiple that is common to both.
Answer
The least common multiple (LCM) of 28 and 24 is $168$.
Answer for screen readers
The least common multiple (LCM) of 28 and 24 is $168$.
Steps to Solve
- Find the prime factorization of each number
For 28, the prime factorization is: $$ 28 = 2^2 \times 7^1 $$
For 24, the prime factorization is: $$ 24 = 2^3 \times 3^1 $$
- Identify the highest powers of each prime factor
List the prime factors involved:
- For the factor 2: the highest power is $2^3$ from 24.
- For the factor 3: the highest power is $3^1$ from 24.
- For the factor 7: the highest power is $7^1$ from 28.
- Multiply the highest powers together
To find the least common multiple (LCM), multiply the highest powers of all prime factors: $$ \text{LCM} = 2^3 \times 3^1 \times 7^1 $$
Calculating this gives: $$ \text{LCM} = 8 \times 3 \times 7 $$
- Complete the multiplication
First, multiply $8 \times 3$: $$ 8 \times 3 = 24 $$
Then, multiply the result by 7: $$ 24 \times 7 = 168 $$
Thus, the least common multiple of 28 and 24 is 168.
The least common multiple (LCM) of 28 and 24 is $168$.
More Information
The LCM is the smallest positive integer that is divisible by both numbers. Finding the LCM is useful in problems involving fractions, scheduling, and finding common denominators.
Tips
- A common mistake is to simply list the multiples of each number instead of using prime factorization, which can lead to incorrect results. To avoid this, always factor the numbers first and take the highest powers of all prime factors.
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