Least Common Multiple (LCM) of 185 and 196
The least common multiple (LCM) of 185 and 196 is 36260.
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 185 and 196?
First, calculate the GCD of 185 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 185 ÷ 196 = 0 remainder 185 |
| 2 | 196 ÷ 185 = 1 remainder 11 |
| 3 | 185 ÷ 11 = 16 remainder 9 |
| 4 | 11 ÷ 9 = 1 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 166 and 150 | 12450 |
| 68 and 117 | 7956 |
| 90 and 116 | 5220 |
| 67 and 31 | 2077 |
| 48 and 51 | 816 |