Least Common Multiple (LCM) of 196 and 170
The least common multiple (LCM) of 196 and 170 is 16660.
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 196 and 170?
First, calculate the GCD of 196 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 196 ÷ 170 = 1 remainder 26 |
| 2 | 170 ÷ 26 = 6 remainder 14 |
| 3 | 26 ÷ 14 = 1 remainder 12 |
| 4 | 14 ÷ 12 = 1 remainder 2 |
| 5 | 12 ÷ 2 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 82 and 187 | 15334 |
| 51 and 42 | 714 |
| 47 and 136 | 6392 |
| 50 and 142 | 3550 |
| 192 and 155 | 29760 |