Least Common Multiple (LCM) of 75 and 161
The least common multiple (LCM) of 75 and 161 is 12075.
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 75 and 161?
First, calculate the GCD of 75 and 161 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 161 = 0 remainder 75 |
| 2 | 161 ÷ 75 = 2 remainder 11 |
| 3 | 75 ÷ 11 = 6 remainder 9 |
| 4 | 11 ÷ 9 = 1 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 157 | 22294 |
| 79 and 24 | 1896 |
| 198 and 161 | 31878 |
| 185 and 38 | 7030 |
| 21 and 134 | 2814 |