Least Common Multiple (LCM) of 83 and 113
The least common multiple (LCM) of 83 and 113 is 9379.
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 113?
First, calculate the GCD of 83 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 113 = 0 remainder 83 |
| 2 | 113 ÷ 83 = 1 remainder 30 |
| 3 | 83 ÷ 30 = 2 remainder 23 |
| 4 | 30 ÷ 23 = 1 remainder 7 |
| 5 | 23 ÷ 7 = 3 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 116 | 3828 |
| 109 and 67 | 7303 |
| 137 and 135 | 18495 |
| 10 and 103 | 1030 |
| 67 and 27 | 1809 |