Least Common Multiple (LCM) of 137 and 190
The least common multiple (LCM) of 137 and 190 is 26030.
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 190?
First, calculate the GCD of 137 and 190 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 190 = 0 remainder 137 |
| 2 | 190 ÷ 137 = 1 remainder 53 |
| 3 | 137 ÷ 53 = 2 remainder 31 |
| 4 | 53 ÷ 31 = 1 remainder 22 |
| 5 | 31 ÷ 22 = 1 remainder 9 |
| 6 | 22 ÷ 9 = 2 remainder 4 |
| 7 | 9 ÷ 4 = 2 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 66 and 65 | 4290 |
| 120 and 125 | 3000 |
| 56 and 55 | 3080 |
| 20 and 46 | 460 |
| 52 and 15 | 780 |