Least Common Multiple (LCM) of 145 and 52
The least common multiple (LCM) of 145 and 52 is 7540.
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 145 and 52?
First, calculate the GCD of 145 and 52 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 145 ÷ 52 = 2 remainder 41 |
| 2 | 52 ÷ 41 = 1 remainder 11 |
| 3 | 41 ÷ 11 = 3 remainder 8 |
| 4 | 11 ÷ 8 = 1 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 |
|---|---|
| 128 and 188 | 6016 |
| 114 and 140 | 7980 |
| 52 and 87 | 4524 |
| 192 and 189 | 12096 |
| 66 and 159 | 3498 |