Least Common Multiple (LCM) of 34 and 134
The least common multiple (LCM) of 34 and 134 is 2278.
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 34 and 134?
First, calculate the GCD of 34 and 134 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 134 = 0 remainder 34 |
| 2 | 134 ÷ 34 = 3 remainder 32 |
| 3 | 34 ÷ 32 = 1 remainder 2 |
| 4 | 32 ÷ 2 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 53 and 129 | 6837 |
| 113 and 95 | 10735 |
| 100 and 68 | 1700 |
| 78 and 91 | 546 |
| 30 and 182 | 2730 |