Least Common Multiple (LCM) of 74 and 89
The least common multiple (LCM) of 74 and 89 is 6586.
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 74 and 89?
First, calculate the GCD of 74 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 74 ÷ 89 = 0 remainder 74 |
| 2 | 89 ÷ 74 = 1 remainder 15 |
| 3 | 74 ÷ 15 = 4 remainder 14 |
| 4 | 15 ÷ 14 = 1 remainder 1 |
| 5 | 14 ÷ 1 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 61 | 6893 |
| 198 and 55 | 990 |
| 149 and 180 | 26820 |
| 138 and 133 | 18354 |
| 144 and 140 | 5040 |