Least Common Multiple (LCM) of 68 and 123
The least common multiple (LCM) of 68 and 123 is 8364.
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 123?
First, calculate the GCD of 68 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 123 = 0 remainder 68 |
| 2 | 123 ÷ 68 = 1 remainder 55 |
| 3 | 68 ÷ 55 = 1 remainder 13 |
| 4 | 55 ÷ 13 = 4 remainder 3 |
| 5 | 13 ÷ 3 = 4 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 95 and 101 | 9595 |
| 90 and 16 | 720 |
| 140 and 188 | 6580 |
| 182 and 21 | 546 |
| 41 and 133 | 5453 |