Least Common Multiple (LCM) of 154 and 100
The least common multiple (LCM) of 154 and 100 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 154 and 100?
First, calculate the GCD of 154 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 154 ÷ 100 = 1 remainder 54 |
| 2 | 100 ÷ 54 = 1 remainder 46 |
| 3 | 54 ÷ 46 = 1 remainder 8 |
| 4 | 46 ÷ 8 = 5 remainder 6 |
| 5 | 8 ÷ 6 = 1 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 21 | 819 |
| 40 and 25 | 200 |
| 83 and 112 | 9296 |
| 175 and 36 | 6300 |
| 197 and 145 | 28565 |