Least Common Multiple (LCM) of 34 and 185
The least common multiple (LCM) of 34 and 185 is 6290.
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 185?
First, calculate the GCD of 34 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 185 = 0 remainder 34 |
| 2 | 185 ÷ 34 = 5 remainder 15 |
| 3 | 34 ÷ 15 = 2 remainder 4 |
| 4 | 15 ÷ 4 = 3 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 167 and 102 | 17034 |
| 110 and 102 | 5610 |
| 192 and 171 | 10944 |
| 128 and 10 | 640 |
| 181 and 111 | 20091 |