Least Common Multiple (LCM) of 50 and 30
The least common multiple (LCM) of 50 and 30 is 150.
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 30?
First, calculate the GCD of 50 and 30 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 50 ÷ 30 = 1 remainder 20 |
| 2 | 30 ÷ 20 = 1 remainder 10 |
| 3 | 20 ÷ 10 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 180 | 18540 |
| 55 and 111 | 6105 |
| 106 and 185 | 19610 |
| 109 and 188 | 20492 |
| 50 and 75 | 150 |