Least Common Multiple (LCM) of 185 and 107
The least common multiple (LCM) of 185 and 107 is 19795.
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 107?
First, calculate the GCD of 185 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 185 ÷ 107 = 1 remainder 78 |
| 2 | 107 ÷ 78 = 1 remainder 29 |
| 3 | 78 ÷ 29 = 2 remainder 20 |
| 4 | 29 ÷ 20 = 1 remainder 9 |
| 5 | 20 ÷ 9 = 2 remainder 2 |
| 6 | 9 ÷ 2 = 4 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 53 and 76 | 4028 |
| 27 and 10 | 270 |
| 138 and 35 | 4830 |
| 138 and 87 | 4002 |
| 129 and 90 | 3870 |