Least Common Multiple (LCM) of 163 and 75
The least common multiple (LCM) of 163 and 75 is 12225.
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 163 and 75?
First, calculate the GCD of 163 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 163 ÷ 75 = 2 remainder 13 |
| 2 | 75 ÷ 13 = 5 remainder 10 |
| 3 | 13 ÷ 10 = 1 remainder 3 |
| 4 | 10 ÷ 3 = 3 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 156 | 9828 |
| 34 and 114 | 1938 |
| 188 and 171 | 32148 |
| 142 and 170 | 12070 |
| 135 and 124 | 16740 |