Least Common Multiple (LCM) of 35 and 134
The least common multiple (LCM) of 35 and 134 is 4690.
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 35 and 134?
First, calculate the GCD of 35 and 134 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 35 ÷ 134 = 0 remainder 35 |
| 2 | 134 ÷ 35 = 3 remainder 29 |
| 3 | 35 ÷ 29 = 1 remainder 6 |
| 4 | 29 ÷ 6 = 4 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 168 and 29 | 4872 |
| 110 and 34 | 1870 |
| 50 and 92 | 2300 |
| 150 and 13 | 1950 |
| 20 and 54 | 540 |