Least Common Multiple (LCM) of 112 and 127
The least common multiple (LCM) of 112 and 127 is 14224.
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 127?
First, calculate the GCD of 112 and 127 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 127 = 0 remainder 112 |
| 2 | 127 ÷ 112 = 1 remainder 15 |
| 3 | 112 ÷ 15 = 7 remainder 7 |
| 4 | 15 ÷ 7 = 2 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 22 and 83 | 1826 |
| 133 and 162 | 21546 |
| 175 and 57 | 9975 |
| 105 and 64 | 6720 |
| 57 and 122 | 6954 |