Least Common Multiple (LCM) of 50 and 123
The least common multiple (LCM) of 50 and 123 is 6150.
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 123?
First, calculate the GCD of 50 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 50 ÷ 123 = 0 remainder 50 |
| 2 | 123 ÷ 50 = 2 remainder 23 |
| 3 | 50 ÷ 23 = 2 remainder 4 |
| 4 | 23 ÷ 4 = 5 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 30 | 300 |
| 75 and 149 | 11175 |
| 78 and 160 | 6240 |
| 36 and 48 | 144 |
| 147 and 50 | 7350 |