Least Common Multiple (LCM) of 123 and 18
The least common multiple (LCM) of 123 and 18 is 738.
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 18?
First, calculate the GCD of 123 and 18 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 18 = 6 remainder 15 |
| 2 | 18 ÷ 15 = 1 remainder 3 |
| 3 | 15 ÷ 3 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 38 and 106 | 2014 |
| 187 and 56 | 10472 |
| 40 and 123 | 4920 |
| 130 and 128 | 8320 |
| 182 and 133 | 3458 |