Least Common Multiple (LCM) of 34 and 91
The least common multiple (LCM) of 34 and 91 is 3094.
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 91?
First, calculate the GCD of 34 and 91 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 91 = 0 remainder 34 |
| 2 | 91 ÷ 34 = 2 remainder 23 |
| 3 | 34 ÷ 23 = 1 remainder 11 |
| 4 | 23 ÷ 11 = 2 remainder 1 |
| 5 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 134 | 14606 |
| 165 and 67 | 11055 |
| 15 and 78 | 390 |
| 156 and 102 | 2652 |
| 197 and 53 | 10441 |