Least Common Multiple (LCM) of 51 and 80
The least common multiple (LCM) of 51 and 80 is 4080.
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 80?
First, calculate the GCD of 51 and 80 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 51 ÷ 80 = 0 remainder 51 |
| 2 | 80 ÷ 51 = 1 remainder 29 |
| 3 | 51 ÷ 29 = 1 remainder 22 |
| 4 | 29 ÷ 22 = 1 remainder 7 |
| 5 | 22 ÷ 7 = 3 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 50 and 119 | 5950 |
| 154 and 68 | 5236 |
| 140 and 153 | 21420 |
| 38 and 60 | 1140 |
| 162 and 164 | 13284 |