Least Common Multiple (LCM) of 193 and 157
The least common multiple (LCM) of 193 and 157 is 30301.
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 193 and 157?
First, calculate the GCD of 193 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 193 ÷ 157 = 1 remainder 36 |
| 2 | 157 ÷ 36 = 4 remainder 13 |
| 3 | 36 ÷ 13 = 2 remainder 10 |
| 4 | 13 ÷ 10 = 1 remainder 3 |
| 5 | 10 ÷ 3 = 3 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 112 | 336 |
| 156 and 109 | 17004 |
| 18 and 112 | 1008 |
| 99 and 177 | 5841 |
| 145 and 129 | 18705 |