Least Common Multiple (LCM) of 123 and 50
The least common multiple (LCM) of 123 and 50 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 123 and 50?
First, calculate the GCD of 123 and 50 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 50 = 2 remainder 23 |
| 2 | 50 ÷ 23 = 2 remainder 4 |
| 3 | 23 ÷ 4 = 5 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 171 and 35 | 5985 |
| 129 and 69 | 2967 |
| 193 and 151 | 29143 |
| 60 and 59 | 3540 |
| 42 and 106 | 2226 |