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 |
|---|---|
| 113 and 135 | 15255 |
| 137 and 110 | 15070 |
| 61 and 74 | 4514 |
| 191 and 112 | 21392 |
| 30 and 113 | 3390 |