Least Common Multiple (LCM) of 190 and 101
The least common multiple (LCM) of 190 and 101 is 19190.
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 101?
First, calculate the GCD of 190 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 190 ÷ 101 = 1 remainder 89 |
| 2 | 101 ÷ 89 = 1 remainder 12 |
| 3 | 89 ÷ 12 = 7 remainder 5 |
| 4 | 12 ÷ 5 = 2 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 57 and 75 | 1425 |
| 111 and 121 | 13431 |
| 99 and 119 | 11781 |
| 192 and 195 | 12480 |
| 35 and 15 | 105 |