Least Common Multiple (LCM) of 117 and 186
The least common multiple (LCM) of 117 and 186 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 117 and 186?
First, calculate the GCD of 117 and 186 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 186 = 0 remainder 117 |
| 2 | 186 ÷ 117 = 1 remainder 69 |
| 3 | 117 ÷ 69 = 1 remainder 48 |
| 4 | 69 ÷ 48 = 1 remainder 21 |
| 5 | 48 ÷ 21 = 2 remainder 6 |
| 6 | 21 ÷ 6 = 3 remainder 3 |
| 7 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 124 and 68 | 2108 |
| 75 and 144 | 3600 |
| 38 and 34 | 646 |
| 172 and 77 | 13244 |
| 112 and 177 | 19824 |