Least Common Multiple (LCM) of 50 and 108
The least common multiple (LCM) of 50 and 108 is 2700.
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 108?
First, calculate the GCD of 50 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 50 ÷ 108 = 0 remainder 50 |
| 2 | 108 ÷ 50 = 2 remainder 8 |
| 3 | 50 ÷ 8 = 6 remainder 2 |
| 4 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 160 and 11 | 1760 |
| 161 and 101 | 16261 |
| 187 and 151 | 28237 |
| 53 and 118 | 6254 |
| 200 and 17 | 3400 |