Least Common Multiple (LCM) of 51 and 171
The least common multiple (LCM) of 51 and 171 is 2907.
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 171?
First, calculate the GCD of 51 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 51 ÷ 171 = 0 remainder 51 |
| 2 | 171 ÷ 51 = 3 remainder 18 |
| 3 | 51 ÷ 18 = 2 remainder 15 |
| 4 | 18 ÷ 15 = 1 remainder 3 |
| 5 | 15 ÷ 3 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 91 | 1820 |
| 123 and 84 | 3444 |
| 119 and 183 | 21777 |
| 98 and 117 | 11466 |
| 37 and 129 | 4773 |