Least Common Multiple (LCM) of 83 and 118
The least common multiple (LCM) of 83 and 118 is 9794.
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 118?
First, calculate the GCD of 83 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 118 = 0 remainder 83 |
| 2 | 118 ÷ 83 = 1 remainder 35 |
| 3 | 83 ÷ 35 = 2 remainder 13 |
| 4 | 35 ÷ 13 = 2 remainder 9 |
| 5 | 13 ÷ 9 = 1 remainder 4 |
| 6 | 9 ÷ 4 = 2 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 25 and 142 | 3550 |
| 106 and 153 | 16218 |
| 103 and 87 | 8961 |
| 45 and 89 | 4005 |
| 192 and 87 | 5568 |