Least Common Multiple (LCM) of 197 and 35
The least common multiple (LCM) of 197 and 35 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 197 and 35?
First, calculate the GCD of 197 and 35 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 197 ÷ 35 = 5 remainder 22 |
| 2 | 35 ÷ 22 = 1 remainder 13 |
| 3 | 22 ÷ 13 = 1 remainder 9 |
| 4 | 13 ÷ 9 = 1 remainder 4 |
| 5 | 9 ÷ 4 = 2 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 156 | 10452 |
| 32 and 135 | 4320 |
| 116 and 162 | 9396 |
| 169 and 135 | 22815 |
| 29 and 132 | 3828 |