Least Common Multiple (LCM) of 102 and 185
The least common multiple (LCM) of 102 and 185 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 102 and 185?
First, calculate the GCD of 102 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 185 = 0 remainder 102 |
| 2 | 185 ÷ 102 = 1 remainder 83 |
| 3 | 102 ÷ 83 = 1 remainder 19 |
| 4 | 83 ÷ 19 = 4 remainder 7 |
| 5 | 19 ÷ 7 = 2 remainder 5 |
| 6 | 7 ÷ 5 = 1 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 126 and 124 | 7812 |
| 110 and 34 | 1870 |
| 164 and 101 | 16564 |
| 160 and 165 | 5280 |
| 23 and 150 | 3450 |