Least Common Multiple (LCM) of 51 and 145
The least common multiple (LCM) of 51 and 145 is 7395.
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 51 and 145?
First, calculate the GCD of 51 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 51 ÷ 145 = 0 remainder 51 |
| 2 | 145 ÷ 51 = 2 remainder 43 |
| 3 | 51 ÷ 43 = 1 remainder 8 |
| 4 | 43 ÷ 8 = 5 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 148 and 128 | 4736 |
| 44 and 136 | 1496 |
| 39 and 168 | 2184 |
| 145 and 96 | 13920 |
| 193 and 57 | 11001 |