Least Common Multiple (LCM) of 138 and 190
The least common multiple (LCM) of 138 and 190 is 13110.
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 138 and 190?
First, calculate the GCD of 138 and 190 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 190 = 0 remainder 138 |
| 2 | 190 ÷ 138 = 1 remainder 52 |
| 3 | 138 ÷ 52 = 2 remainder 34 |
| 4 | 52 ÷ 34 = 1 remainder 18 |
| 5 | 34 ÷ 18 = 1 remainder 16 |
| 6 | 18 ÷ 16 = 1 remainder 2 |
| 7 | 16 ÷ 2 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 89 and 84 | 7476 |
| 123 and 40 | 4920 |
| 157 and 160 | 25120 |
| 89 and 80 | 7120 |
| 45 and 81 | 405 |