Least Common Multiple (LCM) of 188 and 145
The least common multiple (LCM) of 188 and 145 is 27260.
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 145?
First, calculate the GCD of 188 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 188 ÷ 145 = 1 remainder 43 |
| 2 | 145 ÷ 43 = 3 remainder 16 |
| 3 | 43 ÷ 16 = 2 remainder 11 |
| 4 | 16 ÷ 11 = 1 remainder 5 |
| 5 | 11 ÷ 5 = 2 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 68 and 38 | 1292 |
| 60 and 61 | 3660 |
| 79 and 128 | 10112 |
| 170 and 185 | 6290 |
| 13 and 127 | 1651 |