Least Common Multiple (LCM) of 89 and 200
The least common multiple (LCM) of 89 and 200 is 17800.
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 89 and 200?
First, calculate the GCD of 89 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 200 = 0 remainder 89 |
| 2 | 200 ÷ 89 = 2 remainder 22 |
| 3 | 89 ÷ 22 = 4 remainder 1 |
| 4 | 22 ÷ 1 = 22 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 22 | 2398 |
| 120 and 180 | 360 |
| 137 and 173 | 23701 |
| 149 and 167 | 24883 |
| 148 and 29 | 4292 |