Question 7 options:
Find the LCM of these numbers.
10, 12, 15
Type the correct answer.
Blank Space__________
The LCM of 10, 12, and 15 is 60.
To find the least common multiple (LCM) of 10, 12, and 15, we can start by finding the prime factorization of each number:
10 = 2 * 5
12 = 2^2 * 3
15 = 3 * 5
Next, we take the highest exponent of each prime factor and multiply them together:
2^2 * 3 * 5 = 60
Therefore, the LCM of 10, 12, and 15 is 60.
To find the LCM (Least Common Multiple) of the numbers 10, 12, and 15, here is one way to do it:
Step 1: Start by listing the prime factors of each number.
- Prime factors of 10: 2 and 5 (10 = 2 x 5)
- Prime factors of 12: 2, 2, and 3 (12 = 2 x 2 x 3)
- Prime factors of 15: 3 and 5 (15 = 3 x 5)
Step 2: Identify the highest power of each prime factor that appears in any of the numbers.
- The prime factor 2 appears with the highest power of 2 in the number 12.
- The prime factor 3 appears with the highest power of 1 in the number 12.
- The prime factor 5 appears with the highest power of 1 in the number 10 and 15.
Step 3: Multiply these prime factors with their corresponding highest powers.
2^2 x 3^1 x 5^1 = 4 x 3 x 5 = 60
So, the LCM of 10, 12, and 15 is 60.
Therefore, the correct answer is 60.