Least Common Multiple (LCM) of 34 and 23
The least common multiple (LCM) of 34 and 23 is 782.
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 23?
First, calculate the GCD of 34 and 23 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 23 = 1 remainder 11 |
| 2 | 23 ÷ 11 = 2 remainder 1 |
| 3 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 39 and 114 | 1482 |
| 123 and 62 | 7626 |
| 96 and 65 | 6240 |
| 145 and 90 | 2610 |
| 50 and 109 | 5450 |