Least Common Multiple (LCM) of 108 and 50
The least common multiple (LCM) of 108 and 50 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 108 and 50?
First, calculate the GCD of 108 and 50 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 50 = 2 remainder 8 |
| 2 | 50 ÷ 8 = 6 remainder 2 |
| 3 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 186 and 100 | 9300 |
| 23 and 14 | 322 |
| 89 and 96 | 8544 |
| 86 and 16 | 688 |
| 83 and 57 | 4731 |