Least Common Multiple (LCM) of 100 and 112
The least common multiple (LCM) of 100 and 112 is 2800.
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 100 and 112?
First, calculate the GCD of 100 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 112 = 0 remainder 100 |
| 2 | 112 ÷ 100 = 1 remainder 12 |
| 3 | 100 ÷ 12 = 8 remainder 4 |
| 4 | 12 ÷ 4 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 184 | 3312 |
| 156 and 197 | 30732 |
| 27 and 38 | 1026 |
| 18 and 95 | 1710 |
| 183 and 198 | 12078 |