Least Common Multiple (LCM) of 188 and 115
The least common multiple (LCM) of 188 and 115 is 21620.
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 115?
First, calculate the GCD of 188 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 188 ÷ 115 = 1 remainder 73 |
| 2 | 115 ÷ 73 = 1 remainder 42 |
| 3 | 73 ÷ 42 = 1 remainder 31 |
| 4 | 42 ÷ 31 = 1 remainder 11 |
| 5 | 31 ÷ 11 = 2 remainder 9 |
| 6 | 11 ÷ 9 = 1 remainder 2 |
| 7 | 9 ÷ 2 = 4 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 26 | 2990 |
| 158 and 97 | 15326 |
| 80 and 21 | 1680 |
| 33 and 99 | 99 |
| 32 and 45 | 1440 |