Least Common Multiple (LCM) of 191 and 117
The least common multiple (LCM) of 191 and 117 is 22347.
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 191 and 117?
First, calculate the GCD of 191 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 191 ÷ 117 = 1 remainder 74 |
| 2 | 117 ÷ 74 = 1 remainder 43 |
| 3 | 74 ÷ 43 = 1 remainder 31 |
| 4 | 43 ÷ 31 = 1 remainder 12 |
| 5 | 31 ÷ 12 = 2 remainder 7 |
| 6 | 12 ÷ 7 = 1 remainder 5 |
| 7 | 7 ÷ 5 = 1 remainder 2 |
| 8 | 5 ÷ 2 = 2 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 82 and 56 | 2296 |
| 169 and 136 | 22984 |
| 165 and 137 | 22605 |
| 164 and 129 | 21156 |
| 108 and 110 | 5940 |