Least Common Multiple (LCM) of 119 and 81
The least common multiple (LCM) of 119 and 81 is 9639.
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 119 and 81?
First, calculate the GCD of 119 and 81 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 81 = 1 remainder 38 |
| 2 | 81 ÷ 38 = 2 remainder 5 |
| 3 | 38 ÷ 5 = 7 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 |
|---|---|
| 125 and 64 | 8000 |
| 172 and 96 | 4128 |
| 61 and 97 | 5917 |
| 142 and 95 | 13490 |
| 71 and 45 | 3195 |