Least Common Multiple (LCM) of 188 and 39
The least common multiple (LCM) of 188 and 39 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 188 and 39?
First, calculate the GCD of 188 and 39 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 188 ÷ 39 = 4 remainder 32 |
| 2 | 39 ÷ 32 = 1 remainder 7 |
| 3 | 32 ÷ 7 = 4 remainder 4 |
| 4 | 7 ÷ 4 = 1 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 188 and 33 | 6204 |
| 45 and 190 | 1710 |
| 21 and 91 | 273 |
| 61 and 127 | 7747 |
| 113 and 158 | 17854 |