The least common multiple (LCM) of two numbers is the smallest number that is a multiple of both. To find the LCM of 7.56 and 5, we can follow these steps:
Step 1: Convert to Whole Numbers
First, it’s often easier to work with whole numbers. We can convert 7.56 to a whole number by multiplying both 7.56 and 5 by 100, so:
- 7.56 becomes 756
- 5 remains 500
Step 2: Factorization
Next, we need to find the prime factorization of both numbers:
- 756: The prime factors are 2 × 2 × 3 × 3 × 7, which can be written as 22 × 32 × 7.
- 500: The prime factors are 2 × 2 × 5 × 5 × 5, which can be written as 22 × 53.
Step 3: Calculate the LCM
To calculate the LCM, we take the highest power of each prime factor from both factorizations:
- For 2: The highest power is 22.
- For 3: The highest power is 32.
- For 5: The highest power is 53.
- For 7: The highest power is 71.
Step 4: Combine the Highest Powers
Now, we multiply these highest powers together to get the LCM:
LCM = 22 × 32 × 53 × 7 = 75600
Step 5: Convert Back to Original Scale
Since we multiplied by 100 in the beginning, we need to divide the final result by 100 to convert it back:
LCM = 75600 / 100 = 756
Conclusion
Thus, the least common multiple (LCM) of 7.56 and 5 is 756.