Least Common Multiple (LCM) of 18 and 195
The least common multiple (LCM) of 18 and 195 is 1170.
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 18 and 195?
First, calculate the GCD of 18 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 18 ÷ 195 = 0 remainder 18 |
| 2 | 195 ÷ 18 = 10 remainder 15 |
| 3 | 18 ÷ 15 = 1 remainder 3 |
| 4 | 15 ÷ 3 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 51 | 2193 |
| 160 and 159 | 25440 |
| 134 and 123 | 16482 |
| 123 and 22 | 2706 |
| 14 and 152 | 1064 |