Least Common Multiple (LCM) of 115 and 188
The least common multiple (LCM) of 115 and 188 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 115 and 188?
First, calculate the GCD of 115 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 188 = 0 remainder 115 |
| 2 | 188 ÷ 115 = 1 remainder 73 |
| 3 | 115 ÷ 73 = 1 remainder 42 |
| 4 | 73 ÷ 42 = 1 remainder 31 |
| 5 | 42 ÷ 31 = 1 remainder 11 |
| 6 | 31 ÷ 11 = 2 remainder 9 |
| 7 | 11 ÷ 9 = 1 remainder 2 |
| 8 | 9 ÷ 2 = 4 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 57 and 133 | 399 |
| 24 and 74 | 888 |
| 106 and 137 | 14522 |
| 65 and 11 | 715 |
| 166 and 150 | 12450 |