Least Common Multiple (LCM) of 50 and 139
The least common multiple (LCM) of 50 and 139 is 6950.
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 139?
First, calculate the GCD of 50 and 139 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 50 ÷ 139 = 0 remainder 50 |
| 2 | 139 ÷ 50 = 2 remainder 39 |
| 3 | 50 ÷ 39 = 1 remainder 11 |
| 4 | 39 ÷ 11 = 3 remainder 6 |
| 5 | 11 ÷ 6 = 1 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 193 | 26634 |
| 90 and 67 | 6030 |
| 169 and 63 | 10647 |
| 31 and 84 | 2604 |
| 110 and 96 | 5280 |