Least Common Multiple (LCM) of 34 and 192
The least common multiple (LCM) of 34 and 192 is 3264.
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 192?
First, calculate the GCD of 34 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 192 = 0 remainder 34 |
| 2 | 192 ÷ 34 = 5 remainder 22 |
| 3 | 34 ÷ 22 = 1 remainder 12 |
| 4 | 22 ÷ 12 = 1 remainder 10 |
| 5 | 12 ÷ 10 = 1 remainder 2 |
| 6 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 198 and 129 | 8514 |
| 90 and 71 | 6390 |
| 71 and 178 | 12638 |
| 179 and 104 | 18616 |
| 143 and 103 | 14729 |