Least Common Multiple (LCM) of 115 and 189
The least common multiple (LCM) of 115 and 189 is 21735.
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 189?
First, calculate the GCD of 115 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 189 = 0 remainder 115 |
| 2 | 189 ÷ 115 = 1 remainder 74 |
| 3 | 115 ÷ 74 = 1 remainder 41 |
| 4 | 74 ÷ 41 = 1 remainder 33 |
| 5 | 41 ÷ 33 = 1 remainder 8 |
| 6 | 33 ÷ 8 = 4 remainder 1 |
| 7 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 56 and 175 | 1400 |
| 90 and 39 | 1170 |
| 67 and 182 | 12194 |
| 39 and 131 | 5109 |
| 73 and 85 | 6205 |