Least Common Multiple (LCM) of 68 and 75
The least common multiple (LCM) of 68 and 75 is 5100.
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 75?
First, calculate the GCD of 68 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 75 = 0 remainder 68 |
| 2 | 75 ÷ 68 = 1 remainder 7 |
| 3 | 68 ÷ 7 = 9 remainder 5 |
| 4 | 7 ÷ 5 = 1 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 174 and 188 | 16356 |
| 15 and 35 | 105 |
| 12 and 127 | 1524 |
| 143 and 144 | 20592 |
| 172 and 185 | 31820 |