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 |
|---|---|
| 162 and 97 | 15714 |
| 110 and 137 | 15070 |
| 149 and 59 | 8791 |
| 16 and 114 | 912 |
| 42 and 116 | 2436 |