Least Common Multiple (LCM) of 113 and 194
The least common multiple (LCM) of 113 and 194 is 21922.
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 194?
First, calculate the GCD of 113 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 194 = 0 remainder 113 |
| 2 | 194 ÷ 113 = 1 remainder 81 |
| 3 | 113 ÷ 81 = 1 remainder 32 |
| 4 | 81 ÷ 32 = 2 remainder 17 |
| 5 | 32 ÷ 17 = 1 remainder 15 |
| 6 | 17 ÷ 15 = 1 remainder 2 |
| 7 | 15 ÷ 2 = 7 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 131 and 110 | 14410 |
| 73 and 200 | 14600 |
| 36 and 17 | 612 |
| 75 and 199 | 14925 |
| 37 and 51 | 1887 |