Least Common Multiple (LCM) of 50 and 57
The least common multiple (LCM) of 50 and 57 is 2850.
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 57?
First, calculate the GCD of 50 and 57 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 50 ÷ 57 = 0 remainder 50 |
| 2 | 57 ÷ 50 = 1 remainder 7 |
| 3 | 50 ÷ 7 = 7 remainder 1 |
| 4 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 198 and 12 | 396 |
| 116 and 69 | 8004 |
| 115 and 124 | 14260 |
| 14 and 20 | 140 |
| 160 and 74 | 5920 |