Least Common Multiple (LCM) of 83 and 156
The least common multiple (LCM) of 83 and 156 is 12948.
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 156?
First, calculate the GCD of 83 and 156 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 156 = 0 remainder 83 |
| 2 | 156 ÷ 83 = 1 remainder 73 |
| 3 | 83 ÷ 73 = 1 remainder 10 |
| 4 | 73 ÷ 10 = 7 remainder 3 |
| 5 | 10 ÷ 3 = 3 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 169 | 3549 |
| 189 and 166 | 31374 |
| 141 and 183 | 8601 |
| 198 and 29 | 5742 |
| 102 and 149 | 15198 |