Least Common Multiple (LCM) of 123 and 154
The least common multiple (LCM) of 123 and 154 is 18942.
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 154?
First, calculate the GCD of 123 and 154 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 154 = 0 remainder 123 |
| 2 | 154 ÷ 123 = 1 remainder 31 |
| 3 | 123 ÷ 31 = 3 remainder 30 |
| 4 | 31 ÷ 30 = 1 remainder 1 |
| 5 | 30 ÷ 1 = 30 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 62 | 4402 |
| 110 and 90 | 990 |
| 56 and 190 | 5320 |
| 42 and 102 | 714 |
| 72 and 180 | 360 |