Least Common Multiple (LCM) of 28 and 123
The least common multiple (LCM) of 28 and 123 is 3444.
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 28 and 123?
First, calculate the GCD of 28 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 28 ÷ 123 = 0 remainder 28 |
| 2 | 123 ÷ 28 = 4 remainder 11 |
| 3 | 28 ÷ 11 = 2 remainder 6 |
| 4 | 11 ÷ 6 = 1 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 197 and 90 | 17730 |
| 140 and 119 | 2380 |
| 40 and 151 | 6040 |
| 183 and 178 | 32574 |
| 50 and 140 | 700 |