Least Common Multiple (LCM) of 168 and 185
The least common multiple (LCM) of 168 and 185 is 31080.
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 168 and 185?
First, calculate the GCD of 168 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 168 ÷ 185 = 0 remainder 168 |
| 2 | 185 ÷ 168 = 1 remainder 17 |
| 3 | 168 ÷ 17 = 9 remainder 15 |
| 4 | 17 ÷ 15 = 1 remainder 2 |
| 5 | 15 ÷ 2 = 7 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 72 and 64 | 576 |
| 119 and 188 | 22372 |
| 116 and 71 | 8236 |
| 195 and 50 | 1950 |
| 52 and 101 | 5252 |