Least Common Multiple (LCM) of 35 and 197
The least common multiple (LCM) of 35 and 197 is 6895.
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 35 and 197?
First, calculate the GCD of 35 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 35 ÷ 197 = 0 remainder 35 |
| 2 | 197 ÷ 35 = 5 remainder 22 |
| 3 | 35 ÷ 22 = 1 remainder 13 |
| 4 | 22 ÷ 13 = 1 remainder 9 |
| 5 | 13 ÷ 9 = 1 remainder 4 |
| 6 | 9 ÷ 4 = 2 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 117 | 4095 |
| 197 and 152 | 29944 |
| 86 and 89 | 7654 |
| 101 and 194 | 19594 |
| 31 and 182 | 5642 |