Least Common Multiple (LCM) of 137 and 199
The least common multiple (LCM) of 137 and 199 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 137 and 199?
First, calculate the GCD of 137 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 199 = 0 remainder 137 |
| 2 | 199 ÷ 137 = 1 remainder 62 |
| 3 | 137 ÷ 62 = 2 remainder 13 |
| 4 | 62 ÷ 13 = 4 remainder 10 |
| 5 | 13 ÷ 10 = 1 remainder 3 |
| 6 | 10 ÷ 3 = 3 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 126 | 8064 |
| 171 and 129 | 7353 |
| 75 and 131 | 9825 |
| 27 and 53 | 1431 |
| 90 and 71 | 6390 |