Least Common Multiple (LCM) of 149 and 123
The least common multiple (LCM) of 149 and 123 is 18327.
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 149 and 123?
First, calculate the GCD of 149 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 149 ÷ 123 = 1 remainder 26 |
| 2 | 123 ÷ 26 = 4 remainder 19 |
| 3 | 26 ÷ 19 = 1 remainder 7 |
| 4 | 19 ÷ 7 = 2 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 19 and 177 | 3363 |
| 78 and 75 | 1950 |
| 123 and 120 | 4920 |
| 127 and 41 | 5207 |
| 150 and 112 | 8400 |