Least Common Multiple (LCM) of 81 and 119
The least common multiple (LCM) of 81 and 119 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 81 and 119?
First, calculate the GCD of 81 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 81 ÷ 119 = 0 remainder 81 |
| 2 | 119 ÷ 81 = 1 remainder 38 |
| 3 | 81 ÷ 38 = 2 remainder 5 |
| 4 | 38 ÷ 5 = 7 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 111 and 91 | 10101 |
| 25 and 66 | 1650 |
| 13 and 74 | 962 |
| 159 and 135 | 7155 |
| 69 and 124 | 8556 |