Least Common Multiple (LCM) of 101 and 190
The least common multiple (LCM) of 101 and 190 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 101 and 190?
First, calculate the GCD of 101 and 190 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 190 = 0 remainder 101 |
| 2 | 190 ÷ 101 = 1 remainder 89 |
| 3 | 101 ÷ 89 = 1 remainder 12 |
| 4 | 89 ÷ 12 = 7 remainder 5 |
| 5 | 12 ÷ 5 = 2 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 40 and 76 | 760 |
| 186 and 185 | 34410 |
| 173 and 161 | 27853 |
| 137 and 109 | 14933 |
| 26 and 110 | 1430 |