Least Common Multiple (LCM) of 23 and 177
The least common multiple (LCM) of 23 and 177 is 4071.
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 177?
First, calculate the GCD of 23 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 23 ÷ 177 = 0 remainder 23 |
| 2 | 177 ÷ 23 = 7 remainder 16 |
| 3 | 23 ÷ 16 = 1 remainder 7 |
| 4 | 16 ÷ 7 = 2 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 168 and 35 | 840 |
| 154 and 66 | 462 |
| 183 and 45 | 2745 |
| 151 and 17 | 2567 |
| 75 and 99 | 2475 |