Least Common Multiple (LCM) of 167 and 199
The least common multiple (LCM) of 167 and 199 is 33233.
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 167 and 199?
First, calculate the GCD of 167 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 167 ÷ 199 = 0 remainder 167 |
| 2 | 199 ÷ 167 = 1 remainder 32 |
| 3 | 167 ÷ 32 = 5 remainder 7 |
| 4 | 32 ÷ 7 = 4 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 111 and 129 | 4773 |
| 73 and 180 | 13140 |
| 25 and 75 | 75 |
| 40 and 61 | 2440 |
| 55 and 194 | 10670 |