Least Common Multiple (LCM) of 112 and 120
The least common multiple (LCM) of 112 and 120 is 1680.
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 120?
First, calculate the GCD of 112 and 120 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 120 = 0 remainder 112 |
| 2 | 120 ÷ 112 = 1 remainder 8 |
| 3 | 112 ÷ 8 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 150 and 75 | 150 |
| 119 and 186 | 22134 |
| 108 and 198 | 1188 |
| 102 and 92 | 4692 |
| 178 and 103 | 18334 |