Least Common Multiple (LCM) of 51 and 89
The least common multiple (LCM) of 51 and 89 is 4539.
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 51 and 89?
First, calculate the GCD of 51 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 51 ÷ 89 = 0 remainder 51 |
| 2 | 89 ÷ 51 = 1 remainder 38 |
| 3 | 51 ÷ 38 = 1 remainder 13 |
| 4 | 38 ÷ 13 = 2 remainder 12 |
| 5 | 13 ÷ 12 = 1 remainder 1 |
| 6 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 199 and 105 | 20895 |
| 166 and 135 | 22410 |
| 74 and 188 | 6956 |
| 176 and 133 | 23408 |
| 147 and 149 | 21903 |