lcm 15 and 21
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 15 and 21, which is the smallest number that both of these numbers can divide without leaving a remainder.
Answer
The least common multiple of 15 and 21 is 105.
Answer for screen readers
The least common multiple (LCM) of 15 and 21 is 105.
Steps to Solve
- Find the prime factorization of each number
For 15, the prime factors are: $$ 15 = 3 \times 5 $$
For 21, the prime factors are: $$ 21 = 3 \times 7 $$
- Identify the highest powers of each prime factor
We need the highest power of each prime factor from both numbers:
- For the prime factor 3, the highest power is $3^1$ (from both 15 and 21).
- For the prime factor 5, the highest power is $5^1$ (from 15).
- For the prime factor 7, the highest power is $7^1$ (from 21).
- Multiply the highest powers together
Now we can find the least common multiple by multiplying the highest powers: $$ LCM = 3^1 \times 5^1 \times 7^1 $$
- Calculate the LCM
Now we can calculate: $$ LCM = 3 \times 5 \times 7 = 15 \times 7 = 105 $$
The least common multiple (LCM) of 15 and 21 is 105.
More Information
The least common multiple (LCM) is useful for finding common denominators in fractions and is important in various applications in number theory and mathematics. The LCM of two numbers is always greater than or equal to both of the numbers.
Tips
- Forgetting to include all prime factors or their highest powers can lead to an incorrect answer.
- Confusing the least common multiple with the greatest common divisor (GCD) which are different concepts.
