Least Common Multiple (LCM) of 34 and 190
The least common multiple (LCM) of 34 and 190 is 3230.
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 190?
First, calculate the GCD of 34 and 190 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 190 = 0 remainder 34 |
| 2 | 190 ÷ 34 = 5 remainder 20 |
| 3 | 34 ÷ 20 = 1 remainder 14 |
| 4 | 20 ÷ 14 = 1 remainder 6 |
| 5 | 14 ÷ 6 = 2 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 153 | 10251 |
| 65 and 133 | 8645 |
| 59 and 86 | 5074 |
| 73 and 80 | 5840 |
| 49 and 164 | 8036 |