Least Common Multiple (LCM) of 101 and 197
The least common multiple (LCM) of 101 and 197 is 19897.
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 101 and 197?
First, calculate the GCD of 101 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 197 = 0 remainder 101 |
| 2 | 197 ÷ 101 = 1 remainder 96 |
| 3 | 101 ÷ 96 = 1 remainder 5 |
| 4 | 96 ÷ 5 = 19 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 172 and 63 | 10836 |
| 131 and 123 | 16113 |
| 129 and 123 | 5289 |
| 134 and 36 | 2412 |
| 53 and 21 | 1113 |