Least Common Multiple (LCM) of 34 and 46
The least common multiple (LCM) of 34 and 46 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 46?
First, calculate the GCD of 34 and 46 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 46 = 0 remainder 34 |
| 2 | 46 ÷ 34 = 1 remainder 12 |
| 3 | 34 ÷ 12 = 2 remainder 10 |
| 4 | 12 ÷ 10 = 1 remainder 2 |
| 5 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 40 and 123 | 4920 |
| 96 and 11 | 1056 |
| 181 and 176 | 31856 |
| 82 and 105 | 8610 |
| 27 and 110 | 2970 |