Least Common Multiple (LCM) of 110 and 200
The least common multiple (LCM) of 110 and 200 is 2200.
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 110 and 200?
First, calculate the GCD of 110 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 200 = 0 remainder 110 |
| 2 | 200 ÷ 110 = 1 remainder 90 |
| 3 | 110 ÷ 90 = 1 remainder 20 |
| 4 | 90 ÷ 20 = 4 remainder 10 |
| 5 | 20 ÷ 10 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 119 and 95 | 11305 |
| 132 and 161 | 21252 |
| 42 and 184 | 3864 |
| 180 and 136 | 6120 |
| 188 and 177 | 33276 |