Least Common Multiple (LCM) of 45 and 102
The least common multiple (LCM) of 45 and 102 is 1530.
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 102?
First, calculate the GCD of 45 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 102 = 0 remainder 45 |
| 2 | 102 ÷ 45 = 2 remainder 12 |
| 3 | 45 ÷ 12 = 3 remainder 9 |
| 4 | 12 ÷ 9 = 1 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 146 and 93 | 13578 |
| 50 and 176 | 4400 |
| 48 and 24 | 48 |
| 103 and 39 | 4017 |
| 71 and 148 | 10508 |