Least Common Multiple (LCM) of 138 and 197
The least common multiple (LCM) of 138 and 197 is 27186.
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 138 and 197?
First, calculate the GCD of 138 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 197 = 0 remainder 138 |
| 2 | 197 ÷ 138 = 1 remainder 59 |
| 3 | 138 ÷ 59 = 2 remainder 20 |
| 4 | 59 ÷ 20 = 2 remainder 19 |
| 5 | 20 ÷ 19 = 1 remainder 1 |
| 6 | 19 ÷ 1 = 19 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 65 and 23 | 1495 |
| 196 and 151 | 29596 |
| 99 and 89 | 8811 |
| 187 and 187 | 187 |
| 161 and 113 | 18193 |