Least Common Multiple (LCM) of 134 and 75
The least common multiple (LCM) of 134 and 75 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 134 and 75?
First, calculate the GCD of 134 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 134 ÷ 75 = 1 remainder 59 |
| 2 | 75 ÷ 59 = 1 remainder 16 |
| 3 | 59 ÷ 16 = 3 remainder 11 |
| 4 | 16 ÷ 11 = 1 remainder 5 |
| 5 | 11 ÷ 5 = 2 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 93 and 82 | 7626 |
| 164 and 200 | 8200 |
| 165 and 110 | 330 |
| 48 and 76 | 912 |
| 197 and 107 | 21079 |