Least Common Multiple (LCM) of 195 and 58
The least common multiple (LCM) of 195 and 58 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 195 and 58?
First, calculate the GCD of 195 and 58 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 195 ÷ 58 = 3 remainder 21 |
| 2 | 58 ÷ 21 = 2 remainder 16 |
| 3 | 21 ÷ 16 = 1 remainder 5 |
| 4 | 16 ÷ 5 = 3 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 171 and 36 | 684 |
| 103 and 99 | 10197 |
| 190 and 57 | 570 |
| 89 and 137 | 12193 |
| 52 and 143 | 572 |