Least Common Multiple (LCM) of 51 and 172
The least common multiple (LCM) of 51 and 172 is 8772.
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 172?
First, calculate the GCD of 51 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 51 ÷ 172 = 0 remainder 51 |
| 2 | 172 ÷ 51 = 3 remainder 19 |
| 3 | 51 ÷ 19 = 2 remainder 13 |
| 4 | 19 ÷ 13 = 1 remainder 6 |
| 5 | 13 ÷ 6 = 2 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 68 | 7140 |
| 146 and 112 | 8176 |
| 160 and 18 | 1440 |
| 125 and 97 | 12125 |
| 184 and 123 | 22632 |