Least Common Multiple (LCM) of 68 and 192
The least common multiple (LCM) of 68 and 192 is 3264.
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 192?
First, calculate the GCD of 68 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 192 = 0 remainder 68 |
| 2 | 192 ÷ 68 = 2 remainder 56 |
| 3 | 68 ÷ 56 = 1 remainder 12 |
| 4 | 56 ÷ 12 = 4 remainder 8 |
| 5 | 12 ÷ 8 = 1 remainder 4 |
| 6 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 12 | 108 |
| 135 and 44 | 5940 |
| 163 and 48 | 7824 |
| 65 and 70 | 910 |
| 41 and 168 | 6888 |