Least Common Multiple (LCM) of 108 and 34
The least common multiple (LCM) of 108 and 34 is 1836.
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 108 and 34?
First, calculate the GCD of 108 and 34 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 34 = 3 remainder 6 |
| 2 | 34 ÷ 6 = 5 remainder 4 |
| 3 | 6 ÷ 4 = 1 remainder 2 |
| 4 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 65 and 135 | 1755 |
| 95 and 49 | 4655 |
| 61 and 159 | 9699 |
| 148 and 27 | 3996 |
| 132 and 114 | 2508 |