Least Common Multiple (LCM) of 116 and 185
The least common multiple (LCM) of 116 and 185 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 116 and 185?
First, calculate the GCD of 116 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 185 = 0 remainder 116 |
| 2 | 185 ÷ 116 = 1 remainder 69 |
| 3 | 116 ÷ 69 = 1 remainder 47 |
| 4 | 69 ÷ 47 = 1 remainder 22 |
| 5 | 47 ÷ 22 = 2 remainder 3 |
| 6 | 22 ÷ 3 = 7 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 161 | 966 |
| 17 and 125 | 2125 |
| 183 and 93 | 5673 |
| 78 and 50 | 1950 |
| 74 and 153 | 11322 |