Least Common Multiple (LCM) of 60 and 199
The least common multiple (LCM) of 60 and 199 is 11940.
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 60 and 199?
First, calculate the GCD of 60 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 60 ÷ 199 = 0 remainder 60 |
| 2 | 199 ÷ 60 = 3 remainder 19 |
| 3 | 60 ÷ 19 = 3 remainder 3 |
| 4 | 19 ÷ 3 = 6 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 148 and 92 | 3404 |
| 105 and 161 | 2415 |
| 113 and 191 | 21583 |
| 89 and 131 | 11659 |
| 131 and 51 | 6681 |