Least Common Multiple (LCM) of 50 and 91
The least common multiple (LCM) of 50 and 91 is 4550.
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 91?
First, calculate the GCD of 50 and 91 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 50 ÷ 91 = 0 remainder 50 |
| 2 | 91 ÷ 50 = 1 remainder 41 |
| 3 | 50 ÷ 41 = 1 remainder 9 |
| 4 | 41 ÷ 9 = 4 remainder 5 |
| 5 | 9 ÷ 5 = 1 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 76 and 167 | 12692 |
| 140 and 197 | 27580 |
| 18 and 172 | 1548 |
| 21 and 123 | 861 |
| 131 and 78 | 10218 |