Least Common Multiple (LCM) of 83 and 72
The least common multiple (LCM) of 83 and 72 is 5976.
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 72?
First, calculate the GCD of 83 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 72 = 1 remainder 11 |
| 2 | 72 ÷ 11 = 6 remainder 6 |
| 3 | 11 ÷ 6 = 1 remainder 5 |
| 4 | 6 ÷ 5 = 1 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 157 and 91 | 14287 |
| 14 and 83 | 1162 |
| 107 and 86 | 9202 |
| 50 and 197 | 9850 |
| 64 and 113 | 7232 |