Least Common Multiple (LCM) of 112 and 119
The least common multiple (LCM) of 112 and 119 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 119?
First, calculate the GCD of 112 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 119 = 0 remainder 112 |
| 2 | 119 ÷ 112 = 1 remainder 7 |
| 3 | 112 ÷ 7 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 75 and 79 | 5925 |
| 189 and 22 | 4158 |
| 169 and 31 | 5239 |
| 133 and 156 | 20748 |
| 122 and 110 | 6710 |