Least Common Multiple (LCM) of 157 and 112
The least common multiple (LCM) of 157 and 112 is 17584.
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 157 and 112?
First, calculate the GCD of 157 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 112 = 1 remainder 45 |
| 2 | 112 ÷ 45 = 2 remainder 22 |
| 3 | 45 ÷ 22 = 2 remainder 1 |
| 4 | 22 ÷ 1 = 22 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 37 and 66 | 2442 |
| 112 and 130 | 7280 |
| 129 and 97 | 12513 |
| 112 and 112 | 112 |
| 128 and 135 | 17280 |