Least Common Multiple (LCM) of 89 and 123
The least common multiple (LCM) of 89 and 123 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 89 and 123?
First, calculate the GCD of 89 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 123 = 0 remainder 89 |
| 2 | 123 ÷ 89 = 1 remainder 34 |
| 3 | 89 ÷ 34 = 2 remainder 21 |
| 4 | 34 ÷ 21 = 1 remainder 13 |
| 5 | 21 ÷ 13 = 1 remainder 8 |
| 6 | 13 ÷ 8 = 1 remainder 5 |
| 7 | 8 ÷ 5 = 1 remainder 3 |
| 8 | 5 ÷ 3 = 1 remainder 2 |
| 9 | 3 ÷ 2 = 1 remainder 1 |
| 10 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 60 | 4260 |
| 195 and 93 | 6045 |
| 182 and 62 | 5642 |
| 127 and 184 | 23368 |
| 65 and 18 | 1170 |