Least Common Multiple (LCM) of 114 and 21
The least common multiple (LCM) of 114 and 21 is 798.
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 21?
First, calculate the GCD of 114 and 21 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 21 = 5 remainder 9 |
| 2 | 21 ÷ 9 = 2 remainder 3 |
| 3 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 178 | 9612 |
| 118 and 144 | 8496 |
| 179 and 167 | 29893 |
| 104 and 189 | 19656 |
| 144 and 52 | 1872 |