Least Common Multiple (LCM) of 100 and 197
The least common multiple (LCM) of 100 and 197 is 19700.
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 100 and 197?
First, calculate the GCD of 100 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 197 = 0 remainder 100 |
| 2 | 197 ÷ 100 = 1 remainder 97 |
| 3 | 100 ÷ 97 = 1 remainder 3 |
| 4 | 97 ÷ 3 = 32 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 121 and 31 | 3751 |
| 54 and 65 | 3510 |
| 34 and 159 | 5406 |
| 132 and 138 | 3036 |
| 31 and 158 | 4898 |