Least Common Multiple (LCM) of 100 and 108
The least common multiple (LCM) of 100 and 108 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 100 and 108?
First, calculate the GCD of 100 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 108 = 0 remainder 100 |
| 2 | 108 ÷ 100 = 1 remainder 8 |
| 3 | 100 ÷ 8 = 12 remainder 4 |
| 4 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 53 | 2862 |
| 55 and 45 | 495 |
| 127 and 116 | 14732 |
| 134 and 18 | 1206 |
| 59 and 89 | 5251 |