Least Common Multiple (LCM) of 10 and 197
The least common multiple (LCM) of 10 and 197 is 1970.
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 10 and 197?
First, calculate the GCD of 10 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 10 ÷ 197 = 0 remainder 10 |
| 2 | 197 ÷ 10 = 19 remainder 7 |
| 3 | 10 ÷ 7 = 1 remainder 3 |
| 4 | 7 ÷ 3 = 2 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 187 and 68 | 748 |
| 176 and 182 | 16016 |
| 199 and 77 | 15323 |
| 105 and 29 | 3045 |
| 101 and 20 | 2020 |