Least Common Multiple (LCM) of 68 and 185
The least common multiple (LCM) of 68 and 185 is 12580.
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 68 and 185?
First, calculate the GCD of 68 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 185 = 0 remainder 68 |
| 2 | 185 ÷ 68 = 2 remainder 49 |
| 3 | 68 ÷ 49 = 1 remainder 19 |
| 4 | 49 ÷ 19 = 2 remainder 11 |
| 5 | 19 ÷ 11 = 1 remainder 8 |
| 6 | 11 ÷ 8 = 1 remainder 3 |
| 7 | 8 ÷ 3 = 2 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 16 and 96 | 96 |
| 96 and 25 | 2400 |
| 18 and 116 | 1044 |
| 110 and 117 | 12870 |
| 169 and 36 | 6084 |