Least Common Multiple (LCM) of 75 and 164
The least common multiple (LCM) of 75 and 164 is 12300.
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 164?
First, calculate the GCD of 75 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 164 = 0 remainder 75 |
| 2 | 164 ÷ 75 = 2 remainder 14 |
| 3 | 75 ÷ 14 = 5 remainder 5 |
| 4 | 14 ÷ 5 = 2 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 37 and 53 | 1961 |
| 98 and 149 | 14602 |
| 196 and 165 | 32340 |
| 187 and 171 | 31977 |
| 105 and 14 | 210 |