Least Common Multiple (LCM) of 140 and 197
The least common multiple (LCM) of 140 and 197 is 27580.
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 140 and 197?
First, calculate the GCD of 140 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 197 = 0 remainder 140 |
| 2 | 197 ÷ 140 = 1 remainder 57 |
| 3 | 140 ÷ 57 = 2 remainder 26 |
| 4 | 57 ÷ 26 = 2 remainder 5 |
| 5 | 26 ÷ 5 = 5 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 127 | 16383 |
| 118 and 119 | 14042 |
| 18 and 109 | 1962 |
| 105 and 117 | 4095 |
| 27 and 134 | 3618 |