Least Common Multiple (LCM) of 112 and 157
The least common multiple (LCM) of 112 and 157 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 112 and 157?
First, calculate the GCD of 112 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 157 = 0 remainder 112 |
| 2 | 157 ÷ 112 = 1 remainder 45 |
| 3 | 112 ÷ 45 = 2 remainder 22 |
| 4 | 45 ÷ 22 = 2 remainder 1 |
| 5 | 22 ÷ 1 = 22 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 38 and 175 | 6650 |
| 193 and 90 | 17370 |
| 104 and 62 | 3224 |
| 102 and 128 | 6528 |
| 21 and 54 | 378 |