Least Common Multiple (LCM) of 123 and 139
The least common multiple (LCM) of 123 and 139 is 17097.
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 139?
First, calculate the GCD of 123 and 139 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 139 = 0 remainder 123 |
| 2 | 139 ÷ 123 = 1 remainder 16 |
| 3 | 123 ÷ 16 = 7 remainder 11 |
| 4 | 16 ÷ 11 = 1 remainder 5 |
| 5 | 11 ÷ 5 = 2 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 190 and 67 | 12730 |
| 46 and 85 | 3910 |
| 75 and 166 | 12450 |
| 53 and 112 | 5936 |
| 78 and 193 | 15054 |