Least Common Multiple (LCM) of 199 and 137
The least common multiple (LCM) of 199 and 137 is 27263.
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 199 and 137?
First, calculate the GCD of 199 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 137 = 1 remainder 62 |
| 2 | 137 ÷ 62 = 2 remainder 13 |
| 3 | 62 ÷ 13 = 4 remainder 10 |
| 4 | 13 ÷ 10 = 1 remainder 3 |
| 5 | 10 ÷ 3 = 3 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 192 | 13632 |
| 77 and 60 | 4620 |
| 180 and 116 | 5220 |
| 25 and 21 | 525 |
| 73 and 192 | 14016 |