Least Common Multiple (LCM) of 83 and 61
The least common multiple (LCM) of 83 and 61 is 5063.
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 61?
First, calculate the GCD of 83 and 61 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 61 = 1 remainder 22 |
| 2 | 61 ÷ 22 = 2 remainder 17 |
| 3 | 22 ÷ 17 = 1 remainder 5 |
| 4 | 17 ÷ 5 = 3 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 155 and 128 | 19840 |
| 64 and 168 | 1344 |
| 190 and 164 | 15580 |
| 109 and 15 | 1635 |
| 108 and 81 | 324 |