Least Common Multiple (LCM) of 137 and 97
The least common multiple (LCM) of 137 and 97 is 13289.
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 97?
First, calculate the GCD of 137 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 97 = 1 remainder 40 |
| 2 | 97 ÷ 40 = 2 remainder 17 |
| 3 | 40 ÷ 17 = 2 remainder 6 |
| 4 | 17 ÷ 6 = 2 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 58 and 199 | 11542 |
| 55 and 60 | 660 |
| 186 and 113 | 21018 |
| 113 and 137 | 15481 |
| 100 and 73 | 7300 |