Least Common Multiple (LCM) of 96 and 119
The least common multiple (LCM) of 96 and 119 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 96 and 119?
First, calculate the GCD of 96 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 96 ÷ 119 = 0 remainder 96 |
| 2 | 119 ÷ 96 = 1 remainder 23 |
| 3 | 96 ÷ 23 = 4 remainder 4 |
| 4 | 23 ÷ 4 = 5 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 33 and 114 | 1254 |
| 124 and 61 | 7564 |
| 135 and 191 | 25785 |
| 18 and 52 | 468 |
| 173 and 187 | 32351 |