Least Common Multiple (LCM) of 105 and 100
The least common multiple (LCM) of 105 and 100 is 2100.
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 105 and 100?
First, calculate the GCD of 105 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 100 = 1 remainder 5 |
| 2 | 100 ÷ 5 = 20 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 142 | 12638 |
| 67 and 131 | 8777 |
| 102 and 169 | 17238 |
| 54 and 188 | 5076 |
| 135 and 63 | 945 |