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 |
|---|---|
| 120 and 59 | 7080 |
| 196 and 52 | 2548 |
| 52 and 155 | 8060 |
| 113 and 97 | 10961 |
| 27 and 95 | 2565 |