Least Common Multiple (LCM) of 58 and 195
The least common multiple (LCM) of 58 and 195 is 11310.
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 58 and 195?
First, calculate the GCD of 58 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 58 ÷ 195 = 0 remainder 58 |
| 2 | 195 ÷ 58 = 3 remainder 21 |
| 3 | 58 ÷ 21 = 2 remainder 16 |
| 4 | 21 ÷ 16 = 1 remainder 5 |
| 5 | 16 ÷ 5 = 3 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 174 and 123 | 7134 |
| 24 and 60 | 120 |
| 67 and 141 | 9447 |
| 141 and 95 | 13395 |
| 129 and 22 | 2838 |