Least Common Multiple (LCM) of 50 and 110
The least common multiple (LCM) of 50 and 110 is 550.
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 110?
First, calculate the GCD of 50 and 110 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 50 ÷ 110 = 0 remainder 50 |
| 2 | 110 ÷ 50 = 2 remainder 10 |
| 3 | 50 ÷ 10 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 30 | 2040 |
| 13 and 78 | 78 |
| 22 and 76 | 836 |
| 82 and 185 | 15170 |
| 58 and 30 | 870 |