Least Common Multiple (LCM) of 45 and 52
The least common multiple (LCM) of 45 and 52 is 2340.
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 45 and 52?
First, calculate the GCD of 45 and 52 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 52 = 0 remainder 45 |
| 2 | 52 ÷ 45 = 1 remainder 7 |
| 3 | 45 ÷ 7 = 6 remainder 3 |
| 4 | 7 ÷ 3 = 2 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 152 | 4104 |
| 141 and 46 | 6486 |
| 59 and 50 | 2950 |
| 77 and 195 | 15015 |
| 163 and 65 | 10595 |