Least Common Multiple (LCM) of 187 and 199
The least common multiple (LCM) of 187 and 199 is 37213.
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 187 and 199?
First, calculate the GCD of 187 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 187 ÷ 199 = 0 remainder 187 |
| 2 | 199 ÷ 187 = 1 remainder 12 |
| 3 | 187 ÷ 12 = 15 remainder 7 |
| 4 | 12 ÷ 7 = 1 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 67 | 1340 |
| 62 and 115 | 7130 |
| 41 and 142 | 5822 |
| 145 and 172 | 24940 |
| 116 and 64 | 1856 |