Least Common Multiple (LCM) of 108 and 84
The least common multiple (LCM) of 108 and 84 is 756.
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 108 and 84?
First, calculate the GCD of 108 and 84 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 84 = 1 remainder 24 |
| 2 | 84 ÷ 24 = 3 remainder 12 |
| 3 | 24 ÷ 12 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 92 and 197 | 18124 |
| 10 and 15 | 30 |
| 163 and 193 | 31459 |
| 196 and 172 | 8428 |
| 123 and 32 | 3936 |