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 |
|---|---|
| 145 and 81 | 11745 |
| 143 and 119 | 17017 |
| 84 and 189 | 756 |
| 92 and 197 | 18124 |
| 96 and 23 | 2208 |