Least Common Multiple (LCM) of 143 and 83
The least common multiple (LCM) of 143 and 83 is 11869.
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 143 and 83?
First, calculate the GCD of 143 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 143 ÷ 83 = 1 remainder 60 |
| 2 | 83 ÷ 60 = 1 remainder 23 |
| 3 | 60 ÷ 23 = 2 remainder 14 |
| 4 | 23 ÷ 14 = 1 remainder 9 |
| 5 | 14 ÷ 9 = 1 remainder 5 |
| 6 | 9 ÷ 5 = 1 remainder 4 |
| 7 | 5 ÷ 4 = 1 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 176 and 78 | 6864 |
| 44 and 74 | 1628 |
| 31 and 196 | 6076 |
| 22 and 156 | 1716 |
| 17 and 84 | 1428 |