Least Common Multiple (LCM) of 68 and 105
The least common multiple (LCM) of 68 and 105 is 7140.
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 105?
First, calculate the GCD of 68 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 105 = 0 remainder 68 |
| 2 | 105 ÷ 68 = 1 remainder 37 |
| 3 | 68 ÷ 37 = 1 remainder 31 |
| 4 | 37 ÷ 31 = 1 remainder 6 |
| 5 | 31 ÷ 6 = 5 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 181 | 18462 |
| 149 and 152 | 22648 |
| 19 and 115 | 2185 |
| 144 and 24 | 144 |
| 196 and 117 | 22932 |