Least Common Multiple (LCM) of 112 and 57
The least common multiple (LCM) of 112 and 57 is 6384.
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 112 and 57?
First, calculate the GCD of 112 and 57 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 57 = 1 remainder 55 |
| 2 | 57 ÷ 55 = 1 remainder 2 |
| 3 | 55 ÷ 2 = 27 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 42 | 630 |
| 64 and 190 | 6080 |
| 136 and 104 | 1768 |
| 158 and 82 | 6478 |
| 53 and 131 | 6943 |