Least Common Multiple (LCM) of 108 and 68
The least common multiple (LCM) of 108 and 68 is 1836.
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 108 and 68?
First, calculate the GCD of 108 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 68 = 1 remainder 40 |
| 2 | 68 ÷ 40 = 1 remainder 28 |
| 3 | 40 ÷ 28 = 1 remainder 12 |
| 4 | 28 ÷ 12 = 2 remainder 4 |
| 5 | 12 ÷ 4 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 196 | 10388 |
| 61 and 169 | 10309 |
| 168 and 117 | 6552 |
| 119 and 23 | 2737 |
| 115 and 105 | 2415 |