Least Common Multiple (LCM) of 186 and 170
The least common multiple (LCM) of 186 and 170 is 15810.
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 186 and 170?
First, calculate the GCD of 186 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 186 ÷ 170 = 1 remainder 16 |
| 2 | 170 ÷ 16 = 10 remainder 10 |
| 3 | 16 ÷ 10 = 1 remainder 6 |
| 4 | 10 ÷ 6 = 1 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 103 | 11330 |
| 178 and 198 | 17622 |
| 27 and 184 | 4968 |
| 39 and 42 | 546 |
| 98 and 67 | 6566 |