Least Common Multiple (LCM) of 186 and 117
The least common multiple (LCM) of 186 and 117 is 7254.
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 117?
First, calculate the GCD of 186 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 186 ÷ 117 = 1 remainder 69 |
| 2 | 117 ÷ 69 = 1 remainder 48 |
| 3 | 69 ÷ 48 = 1 remainder 21 |
| 4 | 48 ÷ 21 = 2 remainder 6 |
| 5 | 21 ÷ 6 = 3 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 100 | 6700 |
| 34 and 144 | 2448 |
| 109 and 51 | 5559 |
| 15 and 106 | 1590 |
| 179 and 119 | 21301 |