Least Common Multiple (LCM) of 54 and 195
The least common multiple (LCM) of 54 and 195 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 54 and 195?
First, calculate the GCD of 54 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 195 = 0 remainder 54 |
| 2 | 195 ÷ 54 = 3 remainder 33 |
| 3 | 54 ÷ 33 = 1 remainder 21 |
| 4 | 33 ÷ 21 = 1 remainder 12 |
| 5 | 21 ÷ 12 = 1 remainder 9 |
| 6 | 12 ÷ 9 = 1 remainder 3 |
| 7 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 18 | 108 |
| 118 and 50 | 2950 |
| 109 and 199 | 21691 |
| 113 and 195 | 22035 |
| 112 and 148 | 4144 |