Least Common Multiple (LCM) of 172 and 51
The least common multiple (LCM) of 172 and 51 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 172 and 51?
First, calculate the GCD of 172 and 51 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 51 = 3 remainder 19 |
| 2 | 51 ÷ 19 = 2 remainder 13 |
| 3 | 19 ÷ 13 = 1 remainder 6 |
| 4 | 13 ÷ 6 = 2 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 59 and 52 | 3068 |
| 74 and 149 | 11026 |
| 151 and 153 | 23103 |
| 170 and 161 | 27370 |
| 162 and 198 | 1782 |