Least Common Multiple (LCM) of 112 and 68
The least common multiple (LCM) of 112 and 68 is 1904.
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 68?
First, calculate the GCD of 112 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 68 = 1 remainder 44 |
| 2 | 68 ÷ 44 = 1 remainder 24 |
| 3 | 44 ÷ 24 = 1 remainder 20 |
| 4 | 24 ÷ 20 = 1 remainder 4 |
| 5 | 20 ÷ 4 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 157 and 101 | 15857 |
| 43 and 121 | 5203 |
| 122 and 52 | 3172 |
| 176 and 110 | 880 |
| 44 and 58 | 1276 |