Least Common Multiple (LCM) of 154 and 107
The least common multiple (LCM) of 154 and 107 is 16478.
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 107?
First, calculate the GCD of 154 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 154 ÷ 107 = 1 remainder 47 |
| 2 | 107 ÷ 47 = 2 remainder 13 |
| 3 | 47 ÷ 13 = 3 remainder 8 |
| 4 | 13 ÷ 8 = 1 remainder 5 |
| 5 | 8 ÷ 5 = 1 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 191 and 180 | 34380 |
| 181 and 28 | 5068 |
| 50 and 72 | 1800 |
| 64 and 190 | 6080 |
| 193 and 53 | 10229 |