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 |
|---|---|
| 102 and 196 | 9996 |
| 193 and 189 | 36477 |
| 152 and 10 | 760 |
| 150 and 145 | 4350 |
| 50 and 18 | 450 |