Least Common Multiple (LCM) of 102 and 191
The least common multiple (LCM) of 102 and 191 is 19482.
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 102 and 191?
First, calculate the GCD of 102 and 191 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 191 = 0 remainder 102 |
| 2 | 191 ÷ 102 = 1 remainder 89 |
| 3 | 102 ÷ 89 = 1 remainder 13 |
| 4 | 89 ÷ 13 = 6 remainder 11 |
| 5 | 13 ÷ 11 = 1 remainder 2 |
| 6 | 11 ÷ 2 = 5 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 89 and 27 | 2403 |
| 149 and 144 | 21456 |
| 116 and 164 | 4756 |
| 40 and 84 | 840 |
| 160 and 78 | 6240 |