Least Common Multiple (LCM) of 176 and 123
The least common multiple (LCM) of 176 and 123 is 21648.
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 176 and 123?
First, calculate the GCD of 176 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 176 ÷ 123 = 1 remainder 53 |
| 2 | 123 ÷ 53 = 2 remainder 17 |
| 3 | 53 ÷ 17 = 3 remainder 2 |
| 4 | 17 ÷ 2 = 8 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 153 | 17136 |
| 26 and 22 | 286 |
| 102 and 43 | 4386 |
| 184 and 184 | 184 |
| 115 and 159 | 18285 |