Least Common Multiple (LCM) of 103 and 112
The least common multiple (LCM) of 103 and 112 is 11536.
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 103 and 112?
First, calculate the GCD of 103 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 112 = 0 remainder 103 |
| 2 | 112 ÷ 103 = 1 remainder 9 |
| 3 | 103 ÷ 9 = 11 remainder 4 |
| 4 | 9 ÷ 4 = 2 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 53 | 3551 |
| 118 and 108 | 6372 |
| 16 and 197 | 3152 |
| 182 and 125 | 22750 |
| 120 and 107 | 12840 |