What is the LCM of 60 and 24?
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 60 and 24. To find the LCM, we can determine the multiples of each number and find the smallest multiple that they have in common, or we can use their prime factorization.
Answer
$120$
Answer for screen readers
The least common multiple (LCM) of 60 and 24 is $120$.
Steps to Solve
- Find the prime factorization of each number
Begin with the prime factorization of both numbers. For $60$: $$ 60 = 2^2 \times 3^1 \times 5^1 $$
For $24$: $$ 24 = 2^3 \times 3^1 $$
- Identify the highest power of each prime factor
For the LCM, we take the highest power of each prime factor from both factorizations:
- For the prime factor $2$: The highest power is $2^3$ (from 24).
- For the prime factor $3$: The highest power is $3^1$ (from both 60 and 24).
- For the prime factor $5$: The highest power is $5^1$ (from 60).
- Multiply the highest powers together
To find the LCM, multiply these highest powers together:
$$ LCM = 2^3 \times 3^1 \times 5^1 $$
Now, calculate:
$$ LCM = 8 \times 3 \times 5 $$
- Compute the final value
Calculate the product step by step:
First, calculate $8 \times 3 = 24$.
Then multiply by $5$:
$$ LCM = 24 \times 5 = 120 $$
The least common multiple (LCM) of 60 and 24 is $120$.
More Information
The least common multiple (LCM) is the smallest number that is a multiple of both numbers. It is useful in solving problems involving fractions, scheduling, and finding common denominators.
Tips
- Confusing LCM with GCD (Greatest Common Divisor).
- Not considering all prime factors when finding the highest powers.
- Forgetting to multiply all the factors together correctly.