Least Common Multiple (LCM) of 188 and 83
The least common multiple (LCM) of 188 and 83 is 15604.
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 188 and 83?
First, calculate the GCD of 188 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 188 ÷ 83 = 2 remainder 22 |
| 2 | 83 ÷ 22 = 3 remainder 17 |
| 3 | 22 ÷ 17 = 1 remainder 5 |
| 4 | 17 ÷ 5 = 3 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 182 and 39 | 546 |
| 109 and 122 | 13298 |
| 180 and 186 | 5580 |
| 159 and 190 | 30210 |
| 133 and 152 | 1064 |