Least Common Multiple (LCM) of 34 and 105
The least common multiple (LCM) of 34 and 105 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 34 and 105?
First, calculate the GCD of 34 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 105 = 0 remainder 34 |
| 2 | 105 ÷ 34 = 3 remainder 3 |
| 3 | 34 ÷ 3 = 11 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 146 and 71 | 10366 |
| 71 and 122 | 8662 |
| 70 and 14 | 70 |
| 30 and 107 | 3210 |
| 163 and 54 | 8802 |