Least Common Multiple (LCM) of 45 and 124
The least common multiple (LCM) of 45 and 124 is 5580.
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 124?
First, calculate the GCD of 45 and 124 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 124 = 0 remainder 45 |
| 2 | 124 ÷ 45 = 2 remainder 34 |
| 3 | 45 ÷ 34 = 1 remainder 11 |
| 4 | 34 ÷ 11 = 3 remainder 1 |
| 5 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 78 and 78 | 78 |
| 31 and 120 | 3720 |
| 112 and 174 | 9744 |
| 164 and 150 | 12300 |
| 81 and 38 | 3078 |