Least Common Multiple (LCM) of 65 and 154
The least common multiple (LCM) of 65 and 154 is 10010.
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 65 and 154?
First, calculate the GCD of 65 and 154 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 154 = 0 remainder 65 |
| 2 | 154 ÷ 65 = 2 remainder 24 |
| 3 | 65 ÷ 24 = 2 remainder 17 |
| 4 | 24 ÷ 17 = 1 remainder 7 |
| 5 | 17 ÷ 7 = 2 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 60 and 78 | 780 |
| 117 and 85 | 9945 |
| 199 and 111 | 22089 |
| 173 and 166 | 28718 |
| 17 and 64 | 1088 |