Least Common Multiple (LCM) of 189 and 115
The least common multiple (LCM) of 189 and 115 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 189 and 115?
First, calculate the GCD of 189 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 115 = 1 remainder 74 |
| 2 | 115 ÷ 74 = 1 remainder 41 |
| 3 | 74 ÷ 41 = 1 remainder 33 |
| 4 | 41 ÷ 33 = 1 remainder 8 |
| 5 | 33 ÷ 8 = 4 remainder 1 |
| 6 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 18 and 71 | 1278 |
| 170 and 170 | 170 |
| 148 and 194 | 14356 |
| 107 and 30 | 3210 |
| 178 and 160 | 14240 |