Least Common Multiple (LCM) of 59 and 185
The least common multiple (LCM) of 59 and 185 is 10915.
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 185?
First, calculate the GCD of 59 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 185 = 0 remainder 59 |
| 2 | 185 ÷ 59 = 3 remainder 8 |
| 3 | 59 ÷ 8 = 7 remainder 3 |
| 4 | 8 ÷ 3 = 2 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 36 and 177 | 2124 |
| 183 and 194 | 35502 |
| 115 and 80 | 1840 |
| 168 and 123 | 6888 |
| 114 and 114 | 114 |