Least Common Multiple (LCM) of 105 and 34
The least common multiple (LCM) of 105 and 34 is 3570.
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 105 and 34?
First, calculate the GCD of 105 and 34 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 34 = 3 remainder 3 |
| 2 | 34 ÷ 3 = 11 remainder 1 |
| 3 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 172 and 90 | 7740 |
| 147 and 97 | 14259 |
| 10 and 84 | 420 |
| 78 and 156 | 156 |
| 95 and 12 | 1140 |