Least Common Multiple (LCM) of 119 and 84
The least common multiple (LCM) of 119 and 84 is 1428.
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 84?
First, calculate the GCD of 119 and 84 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 84 = 1 remainder 35 |
| 2 | 84 ÷ 35 = 2 remainder 14 |
| 3 | 35 ÷ 14 = 2 remainder 7 |
| 4 | 14 ÷ 7 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 45 | 990 |
| 168 and 76 | 3192 |
| 135 and 63 | 945 |
| 121 and 32 | 3872 |
| 96 and 175 | 16800 |