Least Common Multiple (LCM) of 34 and 199
The least common multiple (LCM) of 34 and 199 is 6766.
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 34 and 199?
First, calculate the GCD of 34 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 199 = 0 remainder 34 |
| 2 | 199 ÷ 34 = 5 remainder 29 |
| 3 | 34 ÷ 29 = 1 remainder 5 |
| 4 | 29 ÷ 5 = 5 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 173 and 65 | 11245 |
| 165 and 88 | 1320 |
| 64 and 167 | 10688 |
| 105 and 108 | 3780 |
| 20 and 54 | 540 |