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 |
|---|---|
| 189 and 140 | 3780 |
| 86 and 37 | 3182 |
| 51 and 56 | 2856 |
| 149 and 138 | 20562 |
| 22 and 10 | 110 |