Least Common Multiple (LCM) of 34 and 92
The least common multiple (LCM) of 34 and 92 is 1564.
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 92?
First, calculate the GCD of 34 and 92 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 92 = 0 remainder 34 |
| 2 | 92 ÷ 34 = 2 remainder 24 |
| 3 | 34 ÷ 24 = 1 remainder 10 |
| 4 | 24 ÷ 10 = 2 remainder 4 |
| 5 | 10 ÷ 4 = 2 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 106 | 13674 |
| 144 and 50 | 3600 |
| 77 and 162 | 12474 |
| 172 and 79 | 13588 |
| 31 and 74 | 2294 |