Least Common Multiple (LCM) of 108 and 100
The least common multiple (LCM) of 108 and 100 is 2700.
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 100?
First, calculate the GCD of 108 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 100 = 1 remainder 8 |
| 2 | 100 ÷ 8 = 12 remainder 4 |
| 3 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 69 | 2691 |
| 37 and 31 | 1147 |
| 180 and 149 | 26820 |
| 135 and 156 | 7020 |
| 84 and 54 | 756 |