Least Common Multiple (LCM) of 45 and 123
The least common multiple (LCM) of 45 and 123 is 1845.
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 123?
First, calculate the GCD of 45 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 123 = 0 remainder 45 |
| 2 | 123 ÷ 45 = 2 remainder 33 |
| 3 | 45 ÷ 33 = 1 remainder 12 |
| 4 | 33 ÷ 12 = 2 remainder 9 |
| 5 | 12 ÷ 9 = 1 remainder 3 |
| 6 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 77 and 96 | 7392 |
| 65 and 134 | 8710 |
| 80 and 123 | 9840 |
| 30 and 110 | 330 |
| 102 and 45 | 1530 |