Least Common Multiple (LCM) of 186 and 67
The least common multiple (LCM) of 186 and 67 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 186 and 67?
First, calculate the GCD of 186 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 186 ÷ 67 = 2 remainder 52 |
| 2 | 67 ÷ 52 = 1 remainder 15 |
| 3 | 52 ÷ 15 = 3 remainder 7 |
| 4 | 15 ÷ 7 = 2 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 88 and 136 | 1496 |
| 65 and 135 | 1755 |
| 38 and 149 | 5662 |
| 126 and 18 | 126 |
| 75 and 78 | 1950 |