Least Common Multiple (LCM) of 59 and 199
The least common multiple (LCM) of 59 and 199 is 11741.
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 199?
First, calculate the GCD of 59 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 199 = 0 remainder 59 |
| 2 | 199 ÷ 59 = 3 remainder 22 |
| 3 | 59 ÷ 22 = 2 remainder 15 |
| 4 | 22 ÷ 15 = 1 remainder 7 |
| 5 | 15 ÷ 7 = 2 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 138 | 14214 |
| 34 and 20 | 340 |
| 65 and 164 | 10660 |
| 27 and 32 | 864 |
| 149 and 119 | 17731 |