Least Common Multiple (LCM) of 76 and 89
The least common multiple (LCM) of 76 and 89 is 6764.
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 76 and 89?
First, calculate the GCD of 76 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 76 ÷ 89 = 0 remainder 76 |
| 2 | 89 ÷ 76 = 1 remainder 13 |
| 3 | 76 ÷ 13 = 5 remainder 11 |
| 4 | 13 ÷ 11 = 1 remainder 2 |
| 5 | 11 ÷ 2 = 5 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 90 | 4770 |
| 22 and 71 | 1562 |
| 165 and 184 | 30360 |
| 185 and 105 | 3885 |
| 170 and 119 | 1190 |