Least Common Multiple (LCM) of 12 and 123
The least common multiple (LCM) of 12 and 123 is 492.
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 12 and 123?
First, calculate the GCD of 12 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 12 ÷ 123 = 0 remainder 12 |
| 2 | 123 ÷ 12 = 10 remainder 3 |
| 3 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 171 and 27 | 513 |
| 167 and 85 | 14195 |
| 37 and 195 | 7215 |
| 177 and 60 | 3540 |
| 176 and 54 | 4752 |