Least Common Multiple (LCM) of 83 and 42
The least common multiple (LCM) of 83 and 42 is 3486.
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 42?
First, calculate the GCD of 83 and 42 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 42 = 1 remainder 41 |
| 2 | 42 ÷ 41 = 1 remainder 1 |
| 3 | 41 ÷ 1 = 41 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 81 and 18 | 162 |
| 108 and 145 | 15660 |
| 93 and 92 | 8556 |
| 85 and 178 | 15130 |
| 151 and 164 | 24764 |