Least Common Multiple (LCM) of 123 and 149
The least common multiple (LCM) of 123 and 149 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 123 and 149?
First, calculate the GCD of 123 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 149 = 0 remainder 123 |
| 2 | 149 ÷ 123 = 1 remainder 26 |
| 3 | 123 ÷ 26 = 4 remainder 19 |
| 4 | 26 ÷ 19 = 1 remainder 7 |
| 5 | 19 ÷ 7 = 2 remainder 5 |
| 6 | 7 ÷ 5 = 1 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 87 and 183 | 5307 |
| 141 and 189 | 8883 |
| 174 and 20 | 1740 |
| 103 and 112 | 11536 |
| 144 and 108 | 432 |