Least Common Multiple (LCM) of 39 and 185
The least common multiple (LCM) of 39 and 185 is 7215.
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 39 and 185?
First, calculate the GCD of 39 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 39 ÷ 185 = 0 remainder 39 |
| 2 | 185 ÷ 39 = 4 remainder 29 |
| 3 | 39 ÷ 29 = 1 remainder 10 |
| 4 | 29 ÷ 10 = 2 remainder 9 |
| 5 | 10 ÷ 9 = 1 remainder 1 |
| 6 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 116 and 164 | 4756 |
| 104 and 174 | 9048 |
| 169 and 111 | 18759 |
| 64 and 125 | 8000 |
| 106 and 131 | 13886 |