Least Common Multiple (LCM) of 68 and 108
The least common multiple (LCM) of 68 and 108 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 68 and 108?
First, calculate the GCD of 68 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 108 = 0 remainder 68 |
| 2 | 108 ÷ 68 = 1 remainder 40 |
| 3 | 68 ÷ 40 = 1 remainder 28 |
| 4 | 40 ÷ 28 = 1 remainder 12 |
| 5 | 28 ÷ 12 = 2 remainder 4 |
| 6 | 12 ÷ 4 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 125 | 22250 |
| 148 and 49 | 7252 |
| 140 and 51 | 7140 |
| 28 and 154 | 308 |
| 182 and 153 | 27846 |