Least Common Multiple (LCM) of 123 and 96
The least common multiple (LCM) of 123 and 96 is 3936.
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 96?
First, calculate the GCD of 123 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 96 = 1 remainder 27 |
| 2 | 96 ÷ 27 = 3 remainder 15 |
| 3 | 27 ÷ 15 = 1 remainder 12 |
| 4 | 15 ÷ 12 = 1 remainder 3 |
| 5 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 150 and 38 | 2850 |
| 86 and 27 | 2322 |
| 123 and 74 | 9102 |
| 118 and 191 | 22538 |
| 13 and 170 | 2210 |