Least Common Multiple (LCM) of 199 and 35
The least common multiple (LCM) of 199 and 35 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 199 and 35?
First, calculate the GCD of 199 and 35 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 35 = 5 remainder 24 |
| 2 | 35 ÷ 24 = 1 remainder 11 |
| 3 | 24 ÷ 11 = 2 remainder 2 |
| 4 | 11 ÷ 2 = 5 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 143 | 25454 |
| 186 and 174 | 5394 |
| 106 and 12 | 636 |
| 37 and 51 | 1887 |
| 124 and 188 | 5828 |