Least Common Multiple (LCM) of 59 and 197
The least common multiple (LCM) of 59 and 197 is 11623.
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 197?
First, calculate the GCD of 59 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 197 = 0 remainder 59 |
| 2 | 197 ÷ 59 = 3 remainder 20 |
| 3 | 59 ÷ 20 = 2 remainder 19 |
| 4 | 20 ÷ 19 = 1 remainder 1 |
| 5 | 19 ÷ 1 = 19 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 187 and 123 | 23001 |
| 167 and 105 | 17535 |
| 165 and 49 | 8085 |
| 155 and 15 | 465 |
| 124 and 190 | 11780 |