Least Common Multiple (LCM) of 100 and 18
The least common multiple (LCM) of 100 and 18 is 900.
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 18?
First, calculate the GCD of 100 and 18 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 18 = 5 remainder 10 |
| 2 | 18 ÷ 10 = 1 remainder 8 |
| 3 | 10 ÷ 8 = 1 remainder 2 |
| 4 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 197 and 166 | 32702 |
| 41 and 197 | 8077 |
| 47 and 88 | 4136 |
| 45 and 117 | 585 |
| 142 and 130 | 9230 |