Least Common Multiple (LCM) of 83 and 186
The least common multiple (LCM) of 83 and 186 is 15438.
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 83 and 186?
First, calculate the GCD of 83 and 186 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 186 = 0 remainder 83 |
| 2 | 186 ÷ 83 = 2 remainder 20 |
| 3 | 83 ÷ 20 = 4 remainder 3 |
| 4 | 20 ÷ 3 = 6 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 87 | 5220 |
| 62 and 96 | 2976 |
| 165 and 61 | 10065 |
| 138 and 53 | 7314 |
| 64 and 152 | 1216 |