Least Common Multiple (LCM) of 119 and 96
The least common multiple (LCM) of 119 and 96 is 11424.
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 119 and 96?
First, calculate the GCD of 119 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 96 = 1 remainder 23 |
| 2 | 96 ÷ 23 = 4 remainder 4 |
| 3 | 23 ÷ 4 = 5 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 173 and 20 | 3460 |
| 182 and 169 | 2366 |
| 66 and 144 | 1584 |
| 96 and 35 | 3360 |
| 87 and 184 | 16008 |