Least Common Multiple (LCM) of 200 and 110
The least common multiple (LCM) of 200 and 110 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 200 and 110?
First, calculate the GCD of 200 and 110 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 200 ÷ 110 = 1 remainder 90 |
| 2 | 110 ÷ 90 = 1 remainder 20 |
| 3 | 90 ÷ 20 = 4 remainder 10 |
| 4 | 20 ÷ 10 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 62 | 3410 |
| 134 and 22 | 1474 |
| 108 and 34 | 1836 |
| 132 and 88 | 264 |
| 31 and 100 | 3100 |