Least Common Multiple (LCM) of 137 and 197
The least common multiple (LCM) of 137 and 197 is 26989.
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 197?
First, calculate the GCD of 137 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 197 = 0 remainder 137 |
| 2 | 197 ÷ 137 = 1 remainder 60 |
| 3 | 137 ÷ 60 = 2 remainder 17 |
| 4 | 60 ÷ 17 = 3 remainder 9 |
| 5 | 17 ÷ 9 = 1 remainder 8 |
| 6 | 9 ÷ 8 = 1 remainder 1 |
| 7 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 104 and 131 | 13624 |
| 49 and 42 | 294 |
| 20 and 59 | 1180 |
| 122 and 91 | 11102 |
| 136 and 200 | 3400 |