Least Common Multiple (LCM) of 199 and 59
The least common multiple (LCM) of 199 and 59 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 199 and 59?
First, calculate the GCD of 199 and 59 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 59 = 3 remainder 22 |
| 2 | 59 ÷ 22 = 2 remainder 15 |
| 3 | 22 ÷ 15 = 1 remainder 7 |
| 4 | 15 ÷ 7 = 2 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 195 and 85 | 3315 |
| 112 and 101 | 11312 |
| 175 and 39 | 6825 |
| 17 and 151 | 2567 |
| 55 and 117 | 6435 |