Least Common Multiple (LCM) of 67 and 186
The least common multiple (LCM) of 67 and 186 is 12462.
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 67 and 186?
First, calculate the GCD of 67 and 186 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 186 = 0 remainder 67 |
| 2 | 186 ÷ 67 = 2 remainder 52 |
| 3 | 67 ÷ 52 = 1 remainder 15 |
| 4 | 52 ÷ 15 = 3 remainder 7 |
| 5 | 15 ÷ 7 = 2 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 135 | 540 |
| 28 and 184 | 1288 |
| 105 and 125 | 2625 |
| 107 and 129 | 13803 |
| 11 and 153 | 1683 |