Least Common Multiple (LCM) of 42 and 83
The least common multiple (LCM) of 42 and 83 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 42 and 83?
First, calculate the GCD of 42 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 83 = 0 remainder 42 |
| 2 | 83 ÷ 42 = 1 remainder 41 |
| 3 | 42 ÷ 41 = 1 remainder 1 |
| 4 | 41 ÷ 1 = 41 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 200 | 3200 |
| 55 and 165 | 165 |
| 37 and 70 | 2590 |
| 64 and 109 | 6976 |
| 85 and 106 | 9010 |