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 |
|---|---|
| 29 and 42 | 1218 |
| 119 and 122 | 14518 |
| 89 and 139 | 12371 |
| 91 and 14 | 182 |
| 185 and 192 | 35520 |