Least Common Multiple (LCM) of 75 and 146
The least common multiple (LCM) of 75 and 146 is 10950.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 75 and 146?
First, calculate the GCD of 75 and 146 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 146 = 0 remainder 75 |
| 2 | 146 ÷ 75 = 1 remainder 71 |
| 3 | 75 ÷ 71 = 1 remainder 4 |
| 4 | 71 ÷ 4 = 17 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 83 and 10 | 830 |
| 66 and 101 | 6666 |
| 53 and 114 | 6042 |
| 149 and 135 | 20115 |
| 121 and 72 | 8712 |