Least Common Multiple (LCM) of 50 and 61
The least common multiple (LCM) of 50 and 61 is 3050.
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 61?
First, calculate the GCD of 50 and 61 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 50 ÷ 61 = 0 remainder 50 |
| 2 | 61 ÷ 50 = 1 remainder 11 |
| 3 | 50 ÷ 11 = 4 remainder 6 |
| 4 | 11 ÷ 6 = 1 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 70 | 350 |
| 89 and 38 | 3382 |
| 46 and 144 | 3312 |
| 186 and 100 | 9300 |
| 76 and 17 | 1292 |