Least Common Multiple (LCM) of 112 and 154
The least common multiple (LCM) of 112 and 154 is 1232.
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 154?
First, calculate the GCD of 112 and 154 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 154 = 0 remainder 112 |
| 2 | 154 ÷ 112 = 1 remainder 42 |
| 3 | 112 ÷ 42 = 2 remainder 28 |
| 4 | 42 ÷ 28 = 1 remainder 14 |
| 5 | 28 ÷ 14 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 173 and 141 | 24393 |
| 30 and 156 | 780 |
| 199 and 13 | 2587 |
| 26 and 115 | 2990 |
| 141 and 172 | 24252 |