Least Common Multiple (LCM) of 195 and 54
The least common multiple (LCM) of 195 and 54 is 3510.
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 195 and 54?
First, calculate the GCD of 195 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 195 ÷ 54 = 3 remainder 33 |
| 2 | 54 ÷ 33 = 1 remainder 21 |
| 3 | 33 ÷ 21 = 1 remainder 12 |
| 4 | 21 ÷ 12 = 1 remainder 9 |
| 5 | 12 ÷ 9 = 1 remainder 3 |
| 6 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 159 and 181 | 28779 |
| 170 and 166 | 14110 |
| 78 and 199 | 15522 |
| 99 and 190 | 18810 |
| 127 and 60 | 7620 |