Least Common Multiple (LCM) of 83 and 200
The least common multiple (LCM) of 83 and 200 is 16600.
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 83 and 200?
First, calculate the GCD of 83 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 200 = 0 remainder 83 |
| 2 | 200 ÷ 83 = 2 remainder 34 |
| 3 | 83 ÷ 34 = 2 remainder 15 |
| 4 | 34 ÷ 15 = 2 remainder 4 |
| 5 | 15 ÷ 4 = 3 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 187 and 10 | 1870 |
| 196 and 124 | 6076 |
| 44 and 68 | 748 |
| 147 and 170 | 24990 |
| 85 and 22 | 1870 |