Least Common Multiple (LCM) of 194 and 113
The least common multiple (LCM) of 194 and 113 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 194 and 113?
First, calculate the GCD of 194 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 194 ÷ 113 = 1 remainder 81 |
| 2 | 113 ÷ 81 = 1 remainder 32 |
| 3 | 81 ÷ 32 = 2 remainder 17 |
| 4 | 32 ÷ 17 = 1 remainder 15 |
| 5 | 17 ÷ 15 = 1 remainder 2 |
| 6 | 15 ÷ 2 = 7 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 67 | 7705 |
| 67 and 102 | 6834 |
| 53 and 190 | 10070 |
| 165 and 57 | 3135 |
| 93 and 161 | 14973 |