Least Common Multiple (LCM) of 83 and 88
The least common multiple (LCM) of 83 and 88 is 7304.
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 88?
First, calculate the GCD of 83 and 88 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 88 = 0 remainder 83 |
| 2 | 88 ÷ 83 = 1 remainder 5 |
| 3 | 83 ÷ 5 = 16 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 66 | 2046 |
| 70 and 74 | 2590 |
| 140 and 91 | 1820 |
| 87 and 165 | 4785 |
| 19 and 163 | 3097 |