Least Common Multiple (LCM) of 185 and 116
The least common multiple (LCM) of 185 and 116 is 21460.
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 185 and 116?
First, calculate the GCD of 185 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 185 ÷ 116 = 1 remainder 69 |
| 2 | 116 ÷ 69 = 1 remainder 47 |
| 3 | 69 ÷ 47 = 1 remainder 22 |
| 4 | 47 ÷ 22 = 2 remainder 3 |
| 5 | 22 ÷ 3 = 7 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 131 and 95 | 12445 |
| 116 and 145 | 580 |
| 102 and 69 | 2346 |
| 29 and 22 | 638 |
| 15 and 185 | 555 |