Least Common Multiple (LCM) of 108 and 191
The least common multiple (LCM) of 108 and 191 is 20628.
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 108 and 191?
First, calculate the GCD of 108 and 191 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 191 = 0 remainder 108 |
| 2 | 191 ÷ 108 = 1 remainder 83 |
| 3 | 108 ÷ 83 = 1 remainder 25 |
| 4 | 83 ÷ 25 = 3 remainder 8 |
| 5 | 25 ÷ 8 = 3 remainder 1 |
| 6 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 35 and 103 | 3605 |
| 136 and 156 | 5304 |
| 155 and 59 | 9145 |
| 36 and 16 | 144 |
| 172 and 191 | 32852 |