Least Common Multiple (LCM) of 83 and 35
The least common multiple (LCM) of 83 and 35 is 2905.
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 35?
First, calculate the GCD of 83 and 35 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 35 = 2 remainder 13 |
| 2 | 35 ÷ 13 = 2 remainder 9 |
| 3 | 13 ÷ 9 = 1 remainder 4 |
| 4 | 9 ÷ 4 = 2 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 71 and 113 | 8023 |
| 105 and 139 | 14595 |
| 32 and 130 | 2080 |
| 144 and 110 | 7920 |
| 98 and 92 | 4508 |