Least Common Multiple (LCM) of 51 and 112
The least common multiple (LCM) of 51 and 112 is 5712.
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 112?
First, calculate the GCD of 51 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 51 ÷ 112 = 0 remainder 51 |
| 2 | 112 ÷ 51 = 2 remainder 10 |
| 3 | 51 ÷ 10 = 5 remainder 1 |
| 4 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 25 and 29 | 725 |
| 114 and 15 | 570 |
| 145 and 135 | 3915 |
| 179 and 13 | 2327 |
| 56 and 116 | 1624 |