Least Common Multiple (LCM) of 60 and 82
The least common multiple (LCM) of 60 and 82 is 2460.
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 60 and 82?
First, calculate the GCD of 60 and 82 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 60 ÷ 82 = 0 remainder 60 |
| 2 | 82 ÷ 60 = 1 remainder 22 |
| 3 | 60 ÷ 22 = 2 remainder 16 |
| 4 | 22 ÷ 16 = 1 remainder 6 |
| 5 | 16 ÷ 6 = 2 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 197 and 90 | 17730 |
| 145 and 92 | 13340 |
| 182 and 195 | 2730 |
| 116 and 45 | 5220 |
| 87 and 64 | 5568 |