Least Common Multiple (LCM) of 191 and 113
The least common multiple (LCM) of 191 and 113 is 21583.
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 113?
First, calculate the GCD of 191 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 191 ÷ 113 = 1 remainder 78 |
| 2 | 113 ÷ 78 = 1 remainder 35 |
| 3 | 78 ÷ 35 = 2 remainder 8 |
| 4 | 35 ÷ 8 = 4 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 167 and 160 | 26720 |
| 162 and 183 | 9882 |
| 90 and 81 | 810 |
| 90 and 136 | 6120 |
| 106 and 175 | 18550 |