Least Common Multiple (LCM) of 93 and 68
The least common multiple (LCM) of 93 and 68 is 6324.
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 93 and 68?
First, calculate the GCD of 93 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 93 ÷ 68 = 1 remainder 25 |
| 2 | 68 ÷ 25 = 2 remainder 18 |
| 3 | 25 ÷ 18 = 1 remainder 7 |
| 4 | 18 ÷ 7 = 2 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 76 and 47 | 3572 |
| 100 and 22 | 1100 |
| 143 and 49 | 7007 |
| 193 and 172 | 33196 |
| 103 and 135 | 13905 |