Least Common Multiple (LCM) of 113 and 195
The least common multiple (LCM) of 113 and 195 is 22035.
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 113 and 195?
First, calculate the GCD of 113 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 195 = 0 remainder 113 |
| 2 | 195 ÷ 113 = 1 remainder 82 |
| 3 | 113 ÷ 82 = 1 remainder 31 |
| 4 | 82 ÷ 31 = 2 remainder 20 |
| 5 | 31 ÷ 20 = 1 remainder 11 |
| 6 | 20 ÷ 11 = 1 remainder 9 |
| 7 | 11 ÷ 9 = 1 remainder 2 |
| 8 | 9 ÷ 2 = 4 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 173 and 11 | 1903 |
| 164 and 29 | 4756 |
| 107 and 29 | 3103 |
| 64 and 63 | 4032 |
| 55 and 83 | 4565 |