Least Common Multiple (LCM) of 197 and 157
The least common multiple (LCM) of 197 and 157 is 30929.
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 197 and 157?
First, calculate the GCD of 197 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 197 ÷ 157 = 1 remainder 40 |
| 2 | 157 ÷ 40 = 3 remainder 37 |
| 3 | 40 ÷ 37 = 1 remainder 3 |
| 4 | 37 ÷ 3 = 12 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 110 | 12870 |
| 55 and 134 | 7370 |
| 161 and 121 | 19481 |
| 30 and 132 | 660 |
| 196 and 122 | 11956 |