Least Common Multiple (LCM) of 123 and 161
The least common multiple (LCM) of 123 and 161 is 19803.
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 161?
First, calculate the GCD of 123 and 161 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 161 = 0 remainder 123 |
| 2 | 161 ÷ 123 = 1 remainder 38 |
| 3 | 123 ÷ 38 = 3 remainder 9 |
| 4 | 38 ÷ 9 = 4 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 12 and 143 | 1716 |
| 135 and 195 | 1755 |
| 149 and 22 | 3278 |
| 72 and 16 | 144 |
| 80 and 57 | 4560 |