Least Common Multiple (LCM) of 68 and 114
The least common multiple (LCM) of 68 and 114 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 68 and 114?
First, calculate the GCD of 68 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 114 = 0 remainder 68 |
| 2 | 114 ÷ 68 = 1 remainder 46 |
| 3 | 68 ÷ 46 = 1 remainder 22 |
| 4 | 46 ÷ 22 = 2 remainder 2 |
| 5 | 22 ÷ 2 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 155 and 196 | 30380 |
| 160 and 106 | 8480 |
| 106 and 143 | 15158 |
| 18 and 133 | 2394 |
| 120 and 56 | 840 |