Least Common Multiple (LCM) of 35 and 199
The least common multiple (LCM) of 35 and 199 is 6965.
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 35 and 199?
First, calculate the GCD of 35 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 35 ÷ 199 = 0 remainder 35 |
| 2 | 199 ÷ 35 = 5 remainder 24 |
| 3 | 35 ÷ 24 = 1 remainder 11 |
| 4 | 24 ÷ 11 = 2 remainder 2 |
| 5 | 11 ÷ 2 = 5 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 89 | 12193 |
| 115 and 195 | 4485 |
| 141 and 141 | 141 |
| 139 and 71 | 9869 |
| 159 and 116 | 18444 |