Least Common Multiple (LCM) of 108 and 190
The least common multiple (LCM) of 108 and 190 is 10260.
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 108 and 190?
First, calculate the GCD of 108 and 190 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 190 = 0 remainder 108 |
| 2 | 190 ÷ 108 = 1 remainder 82 |
| 3 | 108 ÷ 82 = 1 remainder 26 |
| 4 | 82 ÷ 26 = 3 remainder 4 |
| 5 | 26 ÷ 4 = 6 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 189 | 15120 |
| 192 and 37 | 7104 |
| 40 and 154 | 3080 |
| 148 and 19 | 2812 |
| 16 and 56 | 112 |