Least Common Multiple (LCM) of 83 and 187
The least common multiple (LCM) of 83 and 187 is 15521.
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 187?
First, calculate the GCD of 83 and 187 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 187 = 0 remainder 83 |
| 2 | 187 ÷ 83 = 2 remainder 21 |
| 3 | 83 ÷ 21 = 3 remainder 20 |
| 4 | 21 ÷ 20 = 1 remainder 1 |
| 5 | 20 ÷ 1 = 20 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 88 and 65 | 5720 |
| 96 and 84 | 672 |
| 15 and 128 | 1920 |
| 142 and 104 | 7384 |
| 145 and 199 | 28855 |