Least Common Multiple (LCM) of 123 and 14
The least common multiple (LCM) of 123 and 14 is 1722.
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 14?
First, calculate the GCD of 123 and 14 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 14 = 8 remainder 11 |
| 2 | 14 ÷ 11 = 1 remainder 3 |
| 3 | 11 ÷ 3 = 3 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 188 and 116 | 5452 |
| 48 and 139 | 6672 |
| 30 and 106 | 1590 |
| 74 and 128 | 4736 |
| 149 and 193 | 28757 |