Least Common Multiple (LCM) of 59 and 195
The least common multiple (LCM) of 59 and 195 is 11505.
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 59 and 195?
First, calculate the GCD of 59 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 195 = 0 remainder 59 |
| 2 | 195 ÷ 59 = 3 remainder 18 |
| 3 | 59 ÷ 18 = 3 remainder 5 |
| 4 | 18 ÷ 5 = 3 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 125 and 80 | 2000 |
| 151 and 145 | 21895 |
| 150 and 99 | 4950 |
| 184 and 43 | 7912 |
| 18 and 60 | 180 |