Least Common Multiple (LCM) of 140 and 112
The least common multiple (LCM) of 140 and 112 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 140 and 112?
First, calculate the GCD of 140 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 112 = 1 remainder 28 |
| 2 | 112 ÷ 28 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 14 | 910 |
| 155 and 151 | 23405 |
| 189 and 49 | 1323 |
| 182 and 160 | 14560 |
| 17 and 132 | 2244 |