Least Common Multiple (LCM) of 123 and 89
The least common multiple (LCM) of 123 and 89 is 10947.
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 89?
First, calculate the GCD of 123 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 89 = 1 remainder 34 |
| 2 | 89 ÷ 34 = 2 remainder 21 |
| 3 | 34 ÷ 21 = 1 remainder 13 |
| 4 | 21 ÷ 13 = 1 remainder 8 |
| 5 | 13 ÷ 8 = 1 remainder 5 |
| 6 | 8 ÷ 5 = 1 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 185 and 54 | 9990 |
| 139 and 38 | 5282 |
| 181 and 27 | 4887 |
| 174 and 111 | 6438 |
| 101 and 192 | 19392 |