Least Common Multiple (LCM) of 157 and 194
The least common multiple (LCM) of 157 and 194 is 30458.
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 157 and 194?
First, calculate the GCD of 157 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 194 = 0 remainder 157 |
| 2 | 194 ÷ 157 = 1 remainder 37 |
| 3 | 157 ÷ 37 = 4 remainder 9 |
| 4 | 37 ÷ 9 = 4 remainder 1 |
| 5 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 153 and 65 | 9945 |
| 145 and 51 | 7395 |
| 180 and 198 | 1980 |
| 57 and 75 | 1425 |
| 135 and 35 | 945 |