Least Common Multiple (LCM) of 123 and 101
The least common multiple (LCM) of 123 and 101 is 12423.
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 101?
First, calculate the GCD of 123 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 101 = 1 remainder 22 |
| 2 | 101 ÷ 22 = 4 remainder 13 |
| 3 | 22 ÷ 13 = 1 remainder 9 |
| 4 | 13 ÷ 9 = 1 remainder 4 |
| 5 | 9 ÷ 4 = 2 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 165 | 11055 |
| 195 and 71 | 13845 |
| 30 and 86 | 1290 |
| 193 and 37 | 7141 |
| 22 and 85 | 1870 |