Least Common Multiple (LCM) of 23 and 77
The least common multiple (LCM) of 23 and 77 is 1771.
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 77?
First, calculate the GCD of 23 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 23 ÷ 77 = 0 remainder 23 |
| 2 | 77 ÷ 23 = 3 remainder 8 |
| 3 | 23 ÷ 8 = 2 remainder 7 |
| 4 | 8 ÷ 7 = 1 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 143 and 65 | 715 |
| 11 and 24 | 264 |
| 159 and 99 | 5247 |
| 145 and 189 | 27405 |
| 96 and 68 | 1632 |