Least Common Multiple (LCM) of 123 and 160
The least common multiple (LCM) of 123 and 160 is 19680.
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 160?
First, calculate the GCD of 123 and 160 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 160 = 0 remainder 123 |
| 2 | 160 ÷ 123 = 1 remainder 37 |
| 3 | 123 ÷ 37 = 3 remainder 12 |
| 4 | 37 ÷ 12 = 3 remainder 1 |
| 5 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 68 and 166 | 5644 |
| 166 and 17 | 2822 |
| 114 and 135 | 5130 |
| 82 and 152 | 6232 |
| 142 and 21 | 2982 |