Least Common Multiple (LCM) of 123 and 179
The least common multiple (LCM) of 123 and 179 is 22017.
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 123 and 179?
First, calculate the GCD of 123 and 179 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 179 = 0 remainder 123 |
| 2 | 179 ÷ 123 = 1 remainder 56 |
| 3 | 123 ÷ 56 = 2 remainder 11 |
| 4 | 56 ÷ 11 = 5 remainder 1 |
| 5 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 199 and 190 | 37810 |
| 190 and 46 | 4370 |
| 120 and 116 | 3480 |
| 138 and 68 | 4692 |
| 64 and 73 | 4672 |