Least Common Multiple (LCM) of 101 and 185
The least common multiple (LCM) of 101 and 185 is 18685.
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 101 and 185?
First, calculate the GCD of 101 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 185 = 0 remainder 101 |
| 2 | 185 ÷ 101 = 1 remainder 84 |
| 3 | 101 ÷ 84 = 1 remainder 17 |
| 4 | 84 ÷ 17 = 4 remainder 16 |
| 5 | 17 ÷ 16 = 1 remainder 1 |
| 6 | 16 ÷ 1 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 157 and 84 | 13188 |
| 10 and 168 | 840 |
| 65 and 77 | 5005 |
| 134 and 198 | 13266 |
| 100 and 28 | 700 |