Least Common Multiple (LCM) of 100 and 154
The least common multiple (LCM) of 100 and 154 is 7700.
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 154?
First, calculate the GCD of 100 and 154 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 154 = 0 remainder 100 |
| 2 | 154 ÷ 100 = 1 remainder 54 |
| 3 | 100 ÷ 54 = 1 remainder 46 |
| 4 | 54 ÷ 46 = 1 remainder 8 |
| 5 | 46 ÷ 8 = 5 remainder 6 |
| 6 | 8 ÷ 6 = 1 remainder 2 |
| 7 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 174 and 100 | 8700 |
| 60 and 10 | 60 |
| 101 and 54 | 5454 |
| 193 and 106 | 20458 |
| 116 and 123 | 14268 |