Least Common Multiple (LCM) of 75 and 182
The least common multiple (LCM) of 75 and 182 is 13650.
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 182?
First, calculate the GCD of 75 and 182 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 182 = 0 remainder 75 |
| 2 | 182 ÷ 75 = 2 remainder 32 |
| 3 | 75 ÷ 32 = 2 remainder 11 |
| 4 | 32 ÷ 11 = 2 remainder 10 |
| 5 | 11 ÷ 10 = 1 remainder 1 |
| 6 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 193 | 27792 |
| 179 and 198 | 35442 |
| 92 and 170 | 7820 |
| 114 and 85 | 9690 |
| 159 and 112 | 17808 |