Least Common Multiple (LCM) of 114 and 68
The least common multiple (LCM) of 114 and 68 is 3876.
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 68?
First, calculate the GCD of 114 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 68 = 1 remainder 46 |
| 2 | 68 ÷ 46 = 1 remainder 22 |
| 3 | 46 ÷ 22 = 2 remainder 2 |
| 4 | 22 ÷ 2 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 147 | 2793 |
| 149 and 117 | 17433 |
| 57 and 170 | 9690 |
| 20 and 181 | 3620 |
| 164 and 102 | 8364 |