Least Common Multiple (LCM) of 102 and 45
The least common multiple (LCM) of 102 and 45 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 102 and 45?
First, calculate the GCD of 102 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 45 = 2 remainder 12 |
| 2 | 45 ÷ 12 = 3 remainder 9 |
| 3 | 12 ÷ 9 = 1 remainder 3 |
| 4 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 156 and 187 | 29172 |
| 105 and 57 | 1995 |
| 34 and 87 | 2958 |
| 125 and 56 | 7000 |
| 131 and 41 | 5371 |