Least Common Multiple (LCM) of 89 and 56
The least common multiple (LCM) of 89 and 56 is 4984.
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 56?
First, calculate the GCD of 89 and 56 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 56 = 1 remainder 33 |
| 2 | 56 ÷ 33 = 1 remainder 23 |
| 3 | 33 ÷ 23 = 1 remainder 10 |
| 4 | 23 ÷ 10 = 2 remainder 3 |
| 5 | 10 ÷ 3 = 3 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 152 and 46 | 3496 |
| 11 and 137 | 1507 |
| 104 and 29 | 3016 |
| 199 and 17 | 3383 |
| 124 and 144 | 4464 |