Least Common Multiple (LCM) of 39 and 188
The least common multiple (LCM) of 39 and 188 is 7332.
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 188?
First, calculate the GCD of 39 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 39 ÷ 188 = 0 remainder 39 |
| 2 | 188 ÷ 39 = 4 remainder 32 |
| 3 | 39 ÷ 32 = 1 remainder 7 |
| 4 | 32 ÷ 7 = 4 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 87 and 195 | 5655 |
| 53 and 142 | 7526 |
| 173 and 199 | 34427 |
| 10 and 175 | 350 |
| 127 and 130 | 16510 |