Least Common Multiple (LCM) of 114 and 84
The least common multiple (LCM) of 114 and 84 is 1596.
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 114 and 84?
First, calculate the GCD of 114 and 84 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 84 = 1 remainder 30 |
| 2 | 84 ÷ 30 = 2 remainder 24 |
| 3 | 30 ÷ 24 = 1 remainder 6 |
| 4 | 24 ÷ 6 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 35 and 78 | 2730 |
| 199 and 13 | 2587 |
| 52 and 180 | 2340 |
| 21 and 72 | 504 |
| 154 and 118 | 9086 |