Least Common Multiple (LCM) of 123 and 141
The least common multiple (LCM) of 123 and 141 is 5781.
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 141?
First, calculate the GCD of 123 and 141 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 141 = 0 remainder 123 |
| 2 | 141 ÷ 123 = 1 remainder 18 |
| 3 | 123 ÷ 18 = 6 remainder 15 |
| 4 | 18 ÷ 15 = 1 remainder 3 |
| 5 | 15 ÷ 3 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 188 and 28 | 1316 |
| 36 and 72 | 72 |
| 44 and 188 | 2068 |
| 128 and 160 | 640 |
| 143 and 189 | 27027 |