Least Common Multiple (LCM) of 89 and 49
The least common multiple (LCM) of 89 and 49 is 4361.
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 89 and 49?
First, calculate the GCD of 89 and 49 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 49 = 1 remainder 40 |
| 2 | 49 ÷ 40 = 1 remainder 9 |
| 3 | 40 ÷ 9 = 4 remainder 4 |
| 4 | 9 ÷ 4 = 2 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 150 | 900 |
| 134 and 133 | 17822 |
| 128 and 184 | 2944 |
| 74 and 119 | 8806 |
| 199 and 165 | 32835 |