Least Common Multiple (LCM) of 187 and 123
The least common multiple (LCM) of 187 and 123 is 23001.
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 187 and 123?
First, calculate the GCD of 187 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 187 ÷ 123 = 1 remainder 64 |
| 2 | 123 ÷ 64 = 1 remainder 59 |
| 3 | 64 ÷ 59 = 1 remainder 5 |
| 4 | 59 ÷ 5 = 11 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 66 | 2310 |
| 147 and 20 | 2940 |
| 143 and 122 | 17446 |
| 180 and 89 | 16020 |
| 179 and 64 | 11456 |