Least Common Multiple (LCM) of 112 and 117
The least common multiple (LCM) of 112 and 117 is 13104.
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 117?
First, calculate the GCD of 112 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 117 = 0 remainder 112 |
| 2 | 117 ÷ 112 = 1 remainder 5 |
| 3 | 112 ÷ 5 = 22 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 161 and 97 | 15617 |
| 78 and 135 | 3510 |
| 42 and 197 | 8274 |
| 182 and 120 | 10920 |
| 115 and 120 | 2760 |