Least Common Multiple (LCM) of 120 and 81
The least common multiple (LCM) of 120 and 81 is 3240.
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 120 and 81?
First, calculate the GCD of 120 and 81 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 81 = 1 remainder 39 |
| 2 | 81 ÷ 39 = 2 remainder 3 |
| 3 | 39 ÷ 3 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 82 and 78 | 3198 |
| 63 and 55 | 3465 |
| 118 and 119 | 14042 |
| 112 and 162 | 9072 |
| 196 and 42 | 588 |