Least Common Multiple (LCM) of 83 and 64
The least common multiple (LCM) of 83 and 64 is 5312.
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 64?
First, calculate the GCD of 83 and 64 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 64 = 1 remainder 19 |
| 2 | 64 ÷ 19 = 3 remainder 7 |
| 3 | 19 ÷ 7 = 2 remainder 5 |
| 4 | 7 ÷ 5 = 1 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 88 and 25 | 2200 |
| 124 and 191 | 23684 |
| 181 and 52 | 9412 |
| 126 and 155 | 19530 |
| 200 and 49 | 9800 |