Least Common Multiple (LCM) of 185 and 102
The least common multiple (LCM) of 185 and 102 is 18870.
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 102?
First, calculate the GCD of 185 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 185 ÷ 102 = 1 remainder 83 |
| 2 | 102 ÷ 83 = 1 remainder 19 |
| 3 | 83 ÷ 19 = 4 remainder 7 |
| 4 | 19 ÷ 7 = 2 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 18 and 185 | 3330 |
| 108 and 38 | 2052 |
| 55 and 164 | 9020 |
| 197 and 175 | 34475 |
| 25 and 143 | 3575 |