Least Common Multiple (LCM) of 75 and 50
The least common multiple (LCM) of 75 and 50 is 150.
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 50?
First, calculate the GCD of 75 and 50 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 50 = 1 remainder 25 |
| 2 | 50 ÷ 25 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 146 and 15 | 2190 |
| 22 and 145 | 3190 |
| 34 and 178 | 3026 |
| 165 and 81 | 4455 |
| 25 and 56 | 1400 |