Least Common Multiple (LCM) of 117 and 185
The least common multiple (LCM) of 117 and 185 is 21645.
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 185?
First, calculate the GCD of 117 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 185 = 0 remainder 117 |
| 2 | 185 ÷ 117 = 1 remainder 68 |
| 3 | 117 ÷ 68 = 1 remainder 49 |
| 4 | 68 ÷ 49 = 1 remainder 19 |
| 5 | 49 ÷ 19 = 2 remainder 11 |
| 6 | 19 ÷ 11 = 1 remainder 8 |
| 7 | 11 ÷ 8 = 1 remainder 3 |
| 8 | 8 ÷ 3 = 2 remainder 2 |
| 9 | 3 ÷ 2 = 1 remainder 1 |
| 10 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 65 | 1105 |
| 81 and 149 | 12069 |
| 14 and 72 | 504 |
| 71 and 109 | 7739 |
| 142 and 103 | 14626 |