Least Common Multiple (LCM) of 108 and 182
The least common multiple (LCM) of 108 and 182 is 9828.
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 182?
First, calculate the GCD of 108 and 182 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 182 = 0 remainder 108 |
| 2 | 182 ÷ 108 = 1 remainder 74 |
| 3 | 108 ÷ 74 = 1 remainder 34 |
| 4 | 74 ÷ 34 = 2 remainder 6 |
| 5 | 34 ÷ 6 = 5 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 199 and 87 | 17313 |
| 57 and 70 | 3990 |
| 180 and 25 | 900 |
| 80 and 67 | 5360 |
| 116 and 160 | 4640 |