Least Common Multiple (LCM) of 75 and 134
The least common multiple (LCM) of 75 and 134 is 10050.
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 134?
First, calculate the GCD of 75 and 134 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 134 = 0 remainder 75 |
| 2 | 134 ÷ 75 = 1 remainder 59 |
| 3 | 75 ÷ 59 = 1 remainder 16 |
| 4 | 59 ÷ 16 = 3 remainder 11 |
| 5 | 16 ÷ 11 = 1 remainder 5 |
| 6 | 11 ÷ 5 = 2 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 174 | 3480 |
| 123 and 83 | 10209 |
| 168 and 156 | 2184 |
| 193 and 67 | 12931 |
| 200 and 191 | 38200 |