Least Common Multiple (LCM) of 100 and 155
The least common multiple (LCM) of 100 and 155 is 3100.
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 155?
First, calculate the GCD of 100 and 155 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 155 = 0 remainder 100 |
| 2 | 155 ÷ 100 = 1 remainder 55 |
| 3 | 100 ÷ 55 = 1 remainder 45 |
| 4 | 55 ÷ 45 = 1 remainder 10 |
| 5 | 45 ÷ 10 = 4 remainder 5 |
| 6 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 144 | 720 |
| 74 and 174 | 6438 |
| 13 and 105 | 1365 |
| 149 and 31 | 4619 |
| 189 and 146 | 27594 |