Least Common Multiple (LCM) of 157 and 197
The least common multiple (LCM) of 157 and 197 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 157 and 197?
First, calculate the GCD of 157 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 197 = 0 remainder 157 |
| 2 | 197 ÷ 157 = 1 remainder 40 |
| 3 | 157 ÷ 40 = 3 remainder 37 |
| 4 | 40 ÷ 37 = 1 remainder 3 |
| 5 | 37 ÷ 3 = 12 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 40 and 14 | 280 |
| 180 and 112 | 5040 |
| 149 and 90 | 13410 |
| 24 and 98 | 1176 |
| 123 and 11 | 1353 |