Least Common Multiple (LCM) of 50 and 59
The least common multiple (LCM) of 50 and 59 is 2950.
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 59?
First, calculate the GCD of 50 and 59 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 50 ÷ 59 = 0 remainder 50 |
| 2 | 59 ÷ 50 = 1 remainder 9 |
| 3 | 50 ÷ 9 = 5 remainder 5 |
| 4 | 9 ÷ 5 = 1 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 44 and 40 | 440 |
| 168 and 123 | 6888 |
| 134 and 113 | 15142 |
| 79 and 27 | 2133 |
| 163 and 45 | 7335 |