Least Common Multiple (LCM) of 197 and 102
The least common multiple (LCM) of 197 and 102 is 20094.
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 197 and 102?
First, calculate the GCD of 197 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 197 ÷ 102 = 1 remainder 95 |
| 2 | 102 ÷ 95 = 1 remainder 7 |
| 3 | 95 ÷ 7 = 13 remainder 4 |
| 4 | 7 ÷ 4 = 1 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 56 and 112 | 112 |
| 38 and 190 | 190 |
| 127 and 31 | 3937 |
| 48 and 30 | 240 |
| 114 and 93 | 3534 |