Least Common Multiple (LCM) of 23 and 68
The least common multiple (LCM) of 23 and 68 is 1564.
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 23 and 68?
First, calculate the GCD of 23 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 23 ÷ 68 = 0 remainder 23 |
| 2 | 68 ÷ 23 = 2 remainder 22 |
| 3 | 23 ÷ 22 = 1 remainder 1 |
| 4 | 22 ÷ 1 = 22 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 156 and 182 | 1092 |
| 98 and 172 | 8428 |
| 105 and 141 | 4935 |
| 77 and 107 | 8239 |
| 121 and 157 | 18997 |