Least Common Multiple (LCM) of 190 and 111
The least common multiple (LCM) of 190 and 111 is 21090.
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 111?
First, calculate the GCD of 190 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 190 ÷ 111 = 1 remainder 79 |
| 2 | 111 ÷ 79 = 1 remainder 32 |
| 3 | 79 ÷ 32 = 2 remainder 15 |
| 4 | 32 ÷ 15 = 2 remainder 2 |
| 5 | 15 ÷ 2 = 7 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 59 | 6195 |
| 120 and 44 | 1320 |
| 22 and 163 | 3586 |
| 64 and 169 | 10816 |
| 123 and 37 | 4551 |