Least Common Multiple (LCM) of 112 and 140
The least common multiple (LCM) of 112 and 140 is 560.
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 140?
First, calculate the GCD of 112 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 140 = 0 remainder 112 |
| 2 | 140 ÷ 112 = 1 remainder 28 |
| 3 | 112 ÷ 28 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 140 | 420 |
| 107 and 80 | 8560 |
| 182 and 105 | 2730 |
| 195 and 196 | 38220 |
| 134 and 64 | 4288 |