Least Common Multiple (LCM) of 50 and 115
The least common multiple (LCM) of 50 and 115 is 1150.
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 50 and 115?
First, calculate the GCD of 50 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 50 ÷ 115 = 0 remainder 50 |
| 2 | 115 ÷ 50 = 2 remainder 15 |
| 3 | 50 ÷ 15 = 3 remainder 5 |
| 4 | 15 ÷ 5 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 42 | 4578 |
| 188 and 147 | 27636 |
| 65 and 23 | 1495 |
| 195 and 158 | 30810 |
| 68 and 83 | 5644 |