Least Common Multiple (LCM) of 114 and 34
The least common multiple (LCM) of 114 and 34 is 1938.
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 114 and 34?
First, calculate the GCD of 114 and 34 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 34 = 3 remainder 12 |
| 2 | 34 ÷ 12 = 2 remainder 10 |
| 3 | 12 ÷ 10 = 1 remainder 2 |
| 4 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 146 and 66 | 4818 |
| 195 and 37 | 7215 |
| 79 and 102 | 8058 |
| 104 and 176 | 2288 |
| 122 and 138 | 8418 |