Least Common Multiple (LCM) of 100 and 145
The least common multiple (LCM) of 100 and 145 is 2900.
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 145?
First, calculate the GCD of 100 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 145 = 0 remainder 100 |
| 2 | 145 ÷ 100 = 1 remainder 45 |
| 3 | 100 ÷ 45 = 2 remainder 10 |
| 4 | 45 ÷ 10 = 4 remainder 5 |
| 5 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 50 and 108 | 2700 |
| 107 and 140 | 14980 |
| 141 and 35 | 4935 |
| 41 and 147 | 6027 |
| 110 and 24 | 1320 |