Least Common Multiple (LCM) of 34 and 65
The least common multiple (LCM) of 34 and 65 is 2210.
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 65?
First, calculate the GCD of 34 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 65 = 0 remainder 34 |
| 2 | 65 ÷ 34 = 1 remainder 31 |
| 3 | 34 ÷ 31 = 1 remainder 3 |
| 4 | 31 ÷ 3 = 10 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 35 | 140 |
| 131 and 23 | 3013 |
| 35 and 134 | 4690 |
| 170 and 85 | 170 |
| 149 and 75 | 11175 |