Least Common Multiple (LCM) of 83 and 190
The least common multiple (LCM) of 83 and 190 is 15770.
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 83 and 190?
First, calculate the GCD of 83 and 190 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 190 = 0 remainder 83 |
| 2 | 190 ÷ 83 = 2 remainder 24 |
| 3 | 83 ÷ 24 = 3 remainder 11 |
| 4 | 24 ÷ 11 = 2 remainder 2 |
| 5 | 11 ÷ 2 = 5 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 65 and 43 | 2795 |
| 67 and 108 | 7236 |
| 63 and 135 | 945 |
| 160 and 186 | 14880 |
| 79 and 149 | 11771 |