Least Common Multiple (LCM) of 116 and 34
The least common multiple (LCM) of 116 and 34 is 1972.
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 116 and 34?
First, calculate the GCD of 116 and 34 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 34 = 3 remainder 14 |
| 2 | 34 ÷ 14 = 2 remainder 6 |
| 3 | 14 ÷ 6 = 2 remainder 2 |
| 4 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 146 and 91 | 13286 |
| 173 and 34 | 5882 |
| 193 and 181 | 34933 |
| 108 and 56 | 1512 |
| 29 and 67 | 1943 |