Least Common Multiple (LCM) of 101 and 191
The least common multiple (LCM) of 101 and 191 is 19291.
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 191?
First, calculate the GCD of 101 and 191 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 191 = 0 remainder 101 |
| 2 | 191 ÷ 101 = 1 remainder 90 |
| 3 | 101 ÷ 90 = 1 remainder 11 |
| 4 | 90 ÷ 11 = 8 remainder 2 |
| 5 | 11 ÷ 2 = 5 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 153 and 15 | 765 |
| 49 and 182 | 1274 |
| 108 and 120 | 1080 |
| 191 and 113 | 21583 |
| 71 and 101 | 7171 |