Least Common Multiple (LCM) of 190 and 113
The least common multiple (LCM) of 190 and 113 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 190 and 113?
First, calculate the GCD of 190 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 190 ÷ 113 = 1 remainder 77 |
| 2 | 113 ÷ 77 = 1 remainder 36 |
| 3 | 77 ÷ 36 = 2 remainder 5 |
| 4 | 36 ÷ 5 = 7 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 199 and 135 | 26865 |
| 87 and 20 | 1740 |
| 139 and 174 | 24186 |
| 23 and 130 | 2990 |
| 199 and 148 | 29452 |