Least Common Multiple (LCM) of 51 and 162
The least common multiple (LCM) of 51 and 162 is 2754.
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 162?
First, calculate the GCD of 51 and 162 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 51 ÷ 162 = 0 remainder 51 |
| 2 | 162 ÷ 51 = 3 remainder 9 |
| 3 | 51 ÷ 9 = 5 remainder 6 |
| 4 | 9 ÷ 6 = 1 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 77 and 199 | 15323 |
| 167 and 10 | 1670 |
| 70 and 50 | 350 |
| 56 and 46 | 1288 |
| 76 and 71 | 5396 |