Least Common Multiple (LCM) of 105 and 190
The least common multiple (LCM) of 105 and 190 is 3990.
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 105 and 190?
First, calculate the GCD of 105 and 190 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 190 = 0 remainder 105 |
| 2 | 190 ÷ 105 = 1 remainder 85 |
| 3 | 105 ÷ 85 = 1 remainder 20 |
| 4 | 85 ÷ 20 = 4 remainder 5 |
| 5 | 20 ÷ 5 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 77 | 4158 |
| 179 and 105 | 18795 |
| 87 and 71 | 6177 |
| 114 and 91 | 10374 |
| 25 and 82 | 2050 |