Least Common Multiple (LCM) of 60 and 81
The least common multiple (LCM) of 60 and 81 is 1620.
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 81?
First, calculate the GCD of 60 and 81 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 60 ÷ 81 = 0 remainder 60 |
| 2 | 81 ÷ 60 = 1 remainder 21 |
| 3 | 60 ÷ 21 = 2 remainder 18 |
| 4 | 21 ÷ 18 = 1 remainder 3 |
| 5 | 18 ÷ 3 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 160 and 192 | 960 |
| 185 and 103 | 19055 |
| 105 and 156 | 5460 |
| 144 and 34 | 2448 |
| 128 and 128 | 128 |