Least Common Multiple (LCM) of 83 and 132
The least common multiple (LCM) of 83 and 132 is 10956.
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 132?
First, calculate the GCD of 83 and 132 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 132 = 0 remainder 83 |
| 2 | 132 ÷ 83 = 1 remainder 49 |
| 3 | 83 ÷ 49 = 1 remainder 34 |
| 4 | 49 ÷ 34 = 1 remainder 15 |
| 5 | 34 ÷ 15 = 2 remainder 4 |
| 6 | 15 ÷ 4 = 3 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 53 and 10 | 530 |
| 165 and 24 | 1320 |
| 98 and 122 | 5978 |
| 125 and 184 | 23000 |
| 15 and 157 | 2355 |