Least Common Multiple (LCM) of 113 and 190
The least common multiple (LCM) of 113 and 190 is 21470.
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 113 and 190?
First, calculate the GCD of 113 and 190 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 190 = 0 remainder 113 |
| 2 | 190 ÷ 113 = 1 remainder 77 |
| 3 | 113 ÷ 77 = 1 remainder 36 |
| 4 | 77 ÷ 36 = 2 remainder 5 |
| 5 | 36 ÷ 5 = 7 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 188 | 4512 |
| 188 and 30 | 2820 |
| 108 and 37 | 3996 |
| 82 and 184 | 7544 |
| 103 and 200 | 20600 |